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+{"segments": [{"id": 1, "seek": 3204, "start": 19.64, "end": 32.04, "text": "بسم الله الرحمن الرحيم محاضر رقم 29 مساق نظرية الاعداد طلب وطالبات الجامعة الإسلامية قسم رياضيات كلبتي العلوم والتربية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 3714, 5016, 46958, 2288, 12602, 4587, 2304, 9413, 47524, 995, 4587, 8717, 19913, 2288, 10632, 42963, 22488, 18513, 23032, 46152, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 12174, 38251, 12602, 1829, 46958, 1829, 9307, 28242, 3555, 31371, 18863, 1211, 20498, 16070, 2655, 25513, 10632], "avg_logprob": -0.17174257868427342, "compression_ratio": 1.6119402985074627, "no_speech_prob": 8.940696716308594e-07, "words": [{"start": 19.64, "end": 19.98, "word": "بسم", "probability": 0.86279296875}, {"start": 19.98, "end": 20.16, "word": " الله", "probability": 0.96337890625}, {"start": 20.16, "end": 20.54, "word": " الرحمن", "probability": 0.95849609375}, {"start": 20.54, "end": 21.16, "word": " 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divisors", "probability": 0.982421875}, {"start": 129.53, "end": 130.11, "word": " كلهم", "probability": 0.97509765625}, {"start": 130.11, "end": 130.43, "word": " بما", "probability": 0.9794921875}, {"start": 130.43, "end": 130.71, "word": " فيه", "probability": 0.905029296875}, {"start": 130.71, "end": 131.11, "word": " هو", "probability": 0.9794921875}, {"start": 131.11, "end": 131.65, "word": " إيش", "probability": 0.8141276041666666}, {"start": 131.65, "end": 132.45, "word": " حساوة؟", "probability": 0.7821858723958334}], "temperature": 1.0}, {"id": 7, "seek": 15937, "start": 133.79, "end": 159.37, "text": "2n إذاً n أكبر من 0 is called a perfect number if sigma of n بيساوي إيش؟ 2n أو زي ما قلنا في البداية positive integer n is said to be perfect if n is equal to the sum of all its positive divisors excluding n itself i.e. n is perfect if and only if sigma of n بيساوي 2n", "tokens": [17, 77, 11933, 15730, 14111, 297, 5551, 4117, 26890, 9154, 1958, 307, 1219, 257, 2176, 1230, 498, 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150.99, "end": 151.77, "word": " divisors", "probability": 0.98974609375}, {"start": 151.77, "end": 153.09, "word": " excluding", "probability": 0.6826171875}, {"start": 153.09, "end": 153.73, "word": " n", "probability": 0.86865234375}, {"start": 153.73, "end": 154.29, "word": " itself", "probability": 0.6572265625}, {"start": 154.29, "end": 154.63, "word": " i", "probability": 0.2005615234375}, {"start": 154.63, "end": 154.93, "word": ".e.", "probability": 0.988525390625}, {"start": 154.97, "end": 155.29, "word": " n", "probability": 0.83740234375}, {"start": 155.29, "end": 155.55, "word": " is", "probability": 0.96484375}, {"start": 155.55, "end": 156.05, "word": " perfect", "probability": 0.90966796875}, {"start": 156.05, "end": 156.25, "word": " if", "probability": 0.39697265625}, {"start": 156.25, "end": 156.43, "word": " and", "probability": 0.5048828125}, {"start": 156.43, "end": 156.63, "word": " only", "probability": 0.5634765625}, {"start": 156.63, "end": 156.79, "word": " if", "probability": 0.96875}, {"start": 156.79, "end": 157.05, "word": " sigma", "probability": 0.9091796875}, {"start": 157.05, "end": 157.21, "word": " of", "probability": 0.95947265625}, {"start": 157.21, "end": 157.35, "word": " n", "probability": 0.990234375}, {"start": 157.35, "end": 157.93, "word": " بيساوي", "probability": 0.94873046875}, {"start": 157.93, "end": 159.37, "word": " 2n", "probability": 0.964111328125}], "temperature": 1.0}, {"id": 8, "seek": 18620, "start": 161.06, "end": 186.2, "text": "الأعداد الـ Perfect Numbers عزيزة شوية يعني لأ لأن لما نحكي عن الأعداد من واحد لعشر هنلاجينا عدد اللي هو الستة من اللي هو المكوّن من رقمين هنلاجينا التمانية وعشرين تلت أرقام فيه كمان عدد إلى آخره الآن هذه الأعداد اللي هي بدنا نتعرف الآن", "tokens": [6027, 10721, 22488, 18513, 2423, 39184, 10246, 22592, 1616, 6225, 11622, 1829, 11622, 3660, 13412, 2407, 10632, 37495, 22653, 5296, 10721, 5296, 10721, 1863, 5296, 15042, 8717, 5016, 4117, 1829, 18871, 16247, 22488, 18513, 9154, 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{"start": 164.0, "end": 164.86, "word": " عزيزة", "probability": 0.982421875}, {"start": 164.86, "end": 165.34, "word": " شوية", "probability": 0.89453125}, {"start": 165.34, "end": 166.38, "word": " يعني", "probability": 0.8515625}, {"start": 166.38, "end": 166.82, "word": " لأ", "probability": 0.540283203125}, {"start": 166.82, "end": 167.18, "word": " لأن", "probability": 0.5312906901041666}, {"start": 167.18, "end": 167.36, "word": " لما", "probability": 0.75}, {"start": 167.36, "end": 168.2, "word": " نحكي", "probability": 0.98291015625}, {"start": 168.2, "end": 168.4, "word": " عن", "probability": 0.98388671875}, {"start": 168.4, "end": 168.82, "word": " الأعداد", "probability": 0.9812825520833334}, {"start": 168.82, "end": 169.0, "word": " من", "probability": 0.984375}, {"start": 169.0, "end": 169.32, "word": " واحد", "probability": 0.785888671875}, {"start": 169.32, "end": 169.66, "word": " لعشر", "probability": 0.8416341145833334}, {"start": 169.66, "end": 170.28, "word": " هنلاجينا", "probability": 0.6863606770833334}, {"start": 170.28, "end": 170.7, "word": " عدد", "probability": 0.9903971354166666}, {"start": 170.7, "end": 170.84, "word": " اللي", "probability": 0.947509765625}, {"start": 170.84, "end": 171.0, "word": " هو", "probability": 0.98828125}, {"start": 171.0, "end": 171.7, "word": " الستة", "probability": 0.7918294270833334}, {"start": 171.7, "end": 172.62, "word": " من", "probability": 0.947265625}, {"start": 172.62, "end": 173.16, "word": " اللي", "probability": 0.98779296875}, {"start": 173.16, "end": 173.5, "word": " هو", "probability": 0.99267578125}, {"start": 173.5, "end": 174.36, "word": " المكوّن", "probability": 0.82861328125}, {"start": 174.36, "end": 174.52, "word": " من", "probability": 0.99267578125}, {"start": 174.52, "end": 175.1, "word": " رقمين", "probability": 0.9656982421875}, {"start": 175.1, "end": 175.7, "word": " هنلاجينا", "probability": 0.9747721354166666}, {"start": 175.7, "end": 176.14, "word": " التمانية", "probability": 0.78662109375}, {"start": 176.14, "end": 176.76, "word": " وعشرين", "probability": 0.909912109375}, {"start": 176.76, "end": 177.3, "word": " تلت", "probability": 0.8518880208333334}, {"start": 177.3, "end": 177.66, "word": " أرقام", "probability": 0.9913330078125}, {"start": 177.66, "end": 177.92, "word": " فيه", "probability": 0.720458984375}, {"start": 177.92, "end": 178.1, "word": " كمان", "probability": 0.9742838541666666}, {"start": 178.1, "end": 178.5, "word": " عدد", "probability": 0.98876953125}, {"start": 178.5, "end": 178.7, "word": " إلى", "probability": 0.88671875}, {"start": 178.7, "end": 179.22, "word": " آخره", "probability": 0.80517578125}, {"start": 179.22, "end": 180.48, "word": " الآن", "probability": 0.698974609375}, {"start": 180.48, "end": 182.16, "word": " هذه", "probability": 0.8505859375}, {"start": 182.16, "end": 183.04, "word": " الأعداد", "probability": 0.97998046875}, {"start": 183.04, "end": 183.74, "word": " اللي", "probability": 0.984130859375}, {"start": 183.74, "end": 184.12, "word": " هي", "probability": 0.93505859375}, {"start": 184.12, "end": 184.92, "word": " بدنا", "probability": 0.95849609375}, {"start": 184.92, "end": 185.6, "word": " نتعرف", "probability": 0.965576171875}, {"start": 185.6, "end": 186.2, "word": " الآن", "probability": 0.72021484375}], "temperature": 1.0}, {"id": 9, "seek": 20676, "start": 187.16, "end": 206.76, "text": "بقدر الإمكان على طبيعة هذه الأعداد وعلى كيف نودت بعضها أو بعض هذه الأعداد وكيف شكل العدد ال perfect لو كان even لو كان even number", "tokens": [3555, 28543, 2288, 33688, 2304, 41361, 15844, 23032, 21292, 27884, 29538, 16247, 22488, 18513, 4032, 3615, 23942, 9122, 33911, 8717, 23328, 2655, 45030, 11242, 11296, 34051, 45030, 11242, 29538, 16247, 22488, 18513, 4032, 4117, 33911, 13412, 28820, 18863, 3215, 3215, 2423, 2176, 45164, 25961, 754, 45164, 25961, 754, 1230], "avg_logprob": -0.10171874895691872, "compression_ratio": 1.6090225563909775, "no_speech_prob": 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205.82, "end": 206.26, "word": " even", "probability": 0.8251953125}, {"start": 206.26, "end": 206.76, "word": " number", "probability": 0.9765625}], "temperature": 1.0}, {"id": 10, "seek": 21957, "start": 207.47, "end": 219.57, "text": "لو جربنا الـ 6 حسبنا الـ sigma of 6 سنسوى ما هو sigma of 2 أسهل لك في sigma of 3", "tokens": [1211, 2407, 10874, 25513, 8315, 2423, 39184, 1386, 11331, 35457, 8315, 2423, 39184, 12771, 295, 1386, 8608, 1863, 3794, 2407, 7578, 19446, 31439, 12771, 295, 568, 5551, 3794, 3224, 1211, 5296, 4117, 8978, 12771, 295, 805], "avg_logprob": -0.4451013642388421, "compression_ratio": 1.2637362637362637, "no_speech_prob": 2.6226043701171875e-06, "words": [{"start": 207.47, "end": 208.15, "word": "لو", "probability": 0.6641845703125}, {"start": 208.15, "end": 208.71, "word": " جربنا", "probability": 0.833984375}, {"start": 208.71, "end": 209.05, "word": " الـ", "probability": 0.43597412109375}, {"start": 209.05, "end": 209.35, "word": " 6", "probability": 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"probability": 0.62158203125}, {"start": 1262.46, "end": 1262.64, "word": " إيه", "probability": 0.9646809895833334}, {"start": 1262.64, "end": 1263.86, "word": " أشمالها؟", "probability": 0.7800089518229166}, {"start": 1263.86, "end": 1264.82, "word": " قاسمين", "probability": 0.9503173828125}], "temperature": 1.0}, {"id": 50, "seek": 129379, "start": 1265.83, "end": 1293.79, "text": "أو احنا أخدنا نظرية أو ملاحظة أو أخدنا نتيجة ان بي is a prime if and only if it has two divisors او تعريف الـ prime حتى، مظبوط؟ ف sigma of M بتساوي بي زائد واحد if and only if بي is a prime من أكثر من جهة إذا أنا عندي الآن الـ M", "tokens": [10721, 2407, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 8717, 19913, 2288, 10632, 34051, 3714, 15040, 5016, 19913, 3660, 34051, 5551, 9778, 3215, 8315, 8717, 31371, 7435, 3660, 16472, 4724, 1829, 307, 257, 5835, 498, 293, 787, 498, 309, 575, 732, 25974, 830, 1975, 2407, 37279, 16572, 5172, 2423, 39184, 5835, 11331, 49975, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 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نجمع معلوماتنا الان نجمع معلوماتنا صارت عندي الان ال M بتساوي واحد قلت لك واحد ال M هذه بتساوي واحد", "tokens": [10817, 336, 307, 257, 5835, 23758, 36764, 24401, 293, 2423, 39184, 376, 4238, 1975, 1829, 8592, 20666, 3794, 995, 2407, 10632, 36764, 24401, 8717, 7435, 2304, 3615, 20449, 1211, 20498, 9307, 8315, 2423, 7649, 8717, 7435, 2304, 3615, 20449, 1211, 20498, 9307, 8315, 20328, 9640, 2655, 18871, 16254, 2423, 7649, 2423, 376, 39894, 3794, 995, 45865, 36764, 24401, 12174, 1211, 2655, 5296, 4117, 36764, 24401, 2423, 376, 29538, 39894, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.39604167779286703, "compression_ratio": 1.7483443708609272, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1295.48, "end": 1296.2, "word": "small", "probability": 0.773193359375}, {"start": 1296.2, "end": 1296.48, "word": " is", "probability": 0.32470703125}, {"start": 1296.48, "end": 1296.66, "word": " a", "probability": 0.0821533203125}, {"start": 1296.66, "end": 1297.12, "word": " 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الان", "probability": 0.57891845703125}, {"start": 1305.94, "end": 1307.34, "word": " نجمع", "probability": 0.85174560546875}, {"start": 1307.34, "end": 1308.18, "word": " معلوماتنا", "probability": 0.9943359375}, {"start": 1308.18, "end": 1309.46, "word": " صارت", "probability": 0.7845052083333334}, {"start": 1309.46, "end": 1309.8, "word": " عندي", "probability": 0.763671875}, {"start": 1309.8, "end": 1310.34, "word": " الان", "probability": 0.705322265625}, {"start": 1310.34, "end": 1317.46, "word": " ال", "probability": 0.94775390625}, {"start": 1317.46, "end": 1317.62, "word": " M", "probability": 0.884765625}, {"start": 1317.62, "end": 1318.06, "word": " بتساوي", "probability": 0.86962890625}, {"start": 1318.06, "end": 1318.58, "word": " واحد", "probability": 0.984375}, {"start": 1318.58, "end": 1320.3, "word": " قلت", "probability": 0.6364949544270834}, {"start": 1320.3, "end": 1320.44, "word": " لك", "probability": 0.5087890625}, {"start": 1320.44, "end": 1320.7, "word": " واحد", "probability": 0.682861328125}, {"start": 1320.7, "end": 1321.6, "word": " ال", "probability": 0.86474609375}, {"start": 1321.6, "end": 1321.78, "word": " M", "probability": 0.93994140625}, {"start": 1321.78, "end": 1322.0, "word": " هذه", "probability": 0.2802734375}, {"start": 1322.0, "end": 1322.36, "word": " بتساوي", "probability": 0.82843017578125}, {"start": 1322.36, "end": 1322.72, "word": " واحد", "probability": 0.99609375}], "temperature": 1.0}, {"id": 52, "seek": 135307, "start": 1323.39, "end": 1353.07, "text": "إذاً الـ M هذه إيش هتساوي؟ M بيساوي 2K-1 is إبرايم هي واحد اتنين ال M بيساوي 2K-1 في مين؟ في ال M إذاً صالة ال M تبعتنا اللي بديها عبارة عن 2K-1 مضروبة في مين؟ 2K-1", "tokens": [28814, 15730, 14111, 2423, 39184, 376, 29538, 11933, 1829, 8592, 8032, 2655, 3794, 995, 45865, 22807, 376, 4724, 1829, 3794, 995, 45865, 568, 42, 12, 16, 307, 11933, 26890, 995, 32640, 39896, 36764, 24401, 1975, 2655, 1863, 9957, 2423, 376, 4724, 1829, 3794, 995, 45865, 568, 42, 12, 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"end": 1338.37, "word": "-1", "probability": 0.92919921875}, {"start": 1338.37, "end": 1338.59, "word": " في", "probability": 0.5810546875}, {"start": 1338.59, "end": 1339.71, "word": " مين؟", "probability": 0.7869466145833334}, {"start": 1339.71, "end": 1339.83, "word": " في", "probability": 0.947265625}, {"start": 1339.83, "end": 1339.95, "word": " ال", "probability": 0.9599609375}, {"start": 1339.95, "end": 1340.15, "word": " M", "probability": 0.43408203125}, {"start": 1340.15, "end": 1340.69, "word": " إذاً", "probability": 0.7718098958333334}, {"start": 1340.69, "end": 1341.01, "word": " صالة", "probability": 0.8279622395833334}, {"start": 1341.01, "end": 1341.19, "word": " ال", "probability": 0.96826171875}, {"start": 1341.19, "end": 1341.41, "word": " M", "probability": 0.89990234375}, {"start": 1341.41, "end": 1342.11, "word": " تبعتنا", "probability": 0.9366455078125}, {"start": 1342.11, "end": 1342.49, "word": " اللي", "probability": 0.972412109375}, {"start": 1342.49, 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ناقص واحد حيث 2 أُس K ماينس واحد أشمالها is a prime وهو المطلوب", "tokens": [28814, 15730, 5296, 15042, 25961, 2655, 426, 307, 364, 754, 2176, 5835, 1975, 4117, 2655, 2288, 8315, 8717, 4117, 2655, 3555, 426, 15844, 20328, 13063, 3660, 568, 5551, 10859, 3794, 591, 19446, 9957, 3794, 36764, 24401, 8978, 568, 5551, 10859, 3794, 591, 8717, 995, 4587, 9381, 36764, 24401, 11331, 1829, 12984, 568, 5551, 10859, 3794, 591, 19446, 9957, 3794, 36764, 24401, 5551, 8592, 2304, 6027, 11296, 307, 257, 5835, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.2146381590711443, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 1353.86, "end": 1354.26, "word": "إذا", "probability": 0.5438232421875}, {"start": 1354.26, "end": 1354.96, "word": " لما", "probability": 0.891845703125}, {"start": 1354.96, "end": 1356.42, "word": " كانت", "probability": 0.926513671875}, {"start": 1356.42, "end": 1356.74, "word": " N", "probability": 0.3505859375}, {"start": 1356.74, "end": 1357.16, 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تكعيب لأن الـK minus واحد الـK أكبر يساوي مين؟ اتنين يعني الـK مقص واحد أكبر أو يساوي واحد يعني هذا الأُس على الأقل واحد إذا هذا المقدار أكيد أكبر أو يساوي الـA زائد واحد ماشي", "tokens": [28814, 1863, 19446, 25961, 8592, 316, 6055, 2288, 21292, 3660, 34051, 316, 6055, 4117, 3615, 1829, 3555, 5296, 33456, 2423, 39184, 42, 3175, 36764, 24401, 2423, 39184, 42, 5551, 4117, 26890, 7251, 3794, 995, 45865, 3714, 9957, 22807, 1975, 2655, 1863, 9957, 37495, 22653, 2423, 39184, 42, 3714, 4587, 9381, 36764, 24401, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 36764, 24401, 37495, 22653, 23758, 16247, 10859, 3794, 15844, 16247, 4587, 1211, 36764, 24401, 11933, 15730, 23758, 9673, 28543, 9640, 5551, 4117, 25708, 5551, 4117, 26890, 34051, 7251, 3794, 995, 45865, 2423, 39184, 32, 30767, 16373, 3215, 36764, 24401, 3714, 33599, 1829], "avg_logprob": -0.20555219112090695, "compression_ratio": 1.9438202247191012, "no_speech_prob": 7.3909759521484375e-06, "words": [{"start": 1756.25, "end": 1756.53, 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not a prime say that إن الـ K is composite إيش معناه composite؟ إنه في R و S such that الـ K بتساوي R في S و الـ R و الـ S أكبر من 1 وأصغر من مين؟ من الـ K", "tokens": [9778, 1211, 11703, 9381, 8315, 25724, 11622, 38207, 16247, 12610, 47525, 8315, 8717, 12984, 3555, 2655, 5296, 24793, 36145, 2423, 39184, 591, 5551, 8592, 2304, 6027, 11296, 318, 6, 8717, 5172, 2655, 43042, 36145, 2423, 39184, 591, 307, 406, 257, 5835, 584, 300, 36145, 2423, 39184, 591, 307, 25557, 11933, 1829, 8592, 20449, 8315, 3224, 25557, 22807, 36145, 3224, 8978, 497, 4032, 318, 1270, 300, 2423, 39184, 591, 39894, 3794, 995, 45865, 497, 8978, 318, 4032, 2423, 39184, 497, 4032, 2423, 39184, 318, 5551, 4117, 26890, 9154, 502, 36725, 9381, 17082, 2288, 9154, 3714, 9957, 22807, 9154, 2423, 39184, 591], "avg_logprob": -0.2530940688482606, "compression_ratio": 1.6153846153846154, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1830.97, "end": 1831.45, "word": "خلّصنا", "probability": 0.831103515625}, 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"probability": 0.93408203125}, {"start": 1970.86, "end": 1970.86, "word": " تلاتة", "probability": 0.976806640625}, {"start": 1970.86, "end": 1971.04, "word": " او", "probability": 0.915283203125}, {"start": 1971.04, "end": 1971.04, "word": " تلاتة", "probability": 0.98193359375}, {"start": 1971.04, "end": 1972.12, "word": " او", "probability": 0.903564453125}, {"start": 1972.12, "end": 1972.5, "word": " تلاتة", "probability": 0.9844970703125}, {"start": 1972.5, "end": 1974.12, "word": " او", "probability": 0.901123046875}, {"start": 1974.12, "end": 1974.14, "word": " ت", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 77, "seek": 200412, "start": 1976.4, "end": 2004.12, "text": "من واحد ماشي الحال و هذا عندي نفسه أكيد أكبر من مين من واحد عارفين ليش أكبر من واحد لأن هذا أكبر من ايه و أصار زائد واحد زي ما عملنا فوق اللي هو أكبر strictly من مين من واحد إذا صار هذا أكبر من واحد و هذا أكبر من واحد و هذا prime إذا صار contradiction واضح therefore K", "tokens": [27842, 36764, 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{"start": 1977.06, "end": 1977.4, "word": " ماشي", "probability": 0.6238199869791666}, {"start": 1977.4, "end": 1977.82, "word": " الحال", "probability": 0.93017578125}, {"start": 1977.82, "end": 1978.8, "word": " و", "probability": 0.54150390625}, {"start": 1978.8, "end": 1979.2, "word": " هذا", "probability": 0.67236328125}, {"start": 1979.2, "end": 1980.04, "word": " عندي", "probability": 0.6392822265625}, {"start": 1980.04, "end": 1981.42, "word": " نفسه", "probability": 0.9920247395833334}, {"start": 1981.42, "end": 1982.34, "word": " أكيد", "probability": 0.9140625}, {"start": 1982.34, "end": 1982.74, "word": " أكبر", "probability": 0.9601236979166666}, {"start": 1982.74, "end": 1982.94, "word": " من", "probability": 0.9912109375}, {"start": 1982.94, "end": 1983.46, "word": " مين", "probability": 0.86767578125}, {"start": 1983.46, "end": 1984.56, "word": " من", "probability": 0.59326171875}, {"start": 1984.56, "end": 1985.04, "word": " واحد", "probability": 0.992919921875}, {"start": 1985.04, "end": 1986.18, "word": " عارفين", "probability": 0.9359130859375}, {"start": 1986.18, "end": 1986.4, "word": " ليش", "probability": 0.9130859375}, {"start": 1986.4, "end": 1986.62, "word": " أكبر", "probability": 0.9671223958333334}, {"start": 1986.62, "end": 1986.74, "word": " من", "probability": 0.994140625}, {"start": 1986.74, "end": 1987.2, "word": " واحد", "probability": 0.9931640625}, {"start": 1987.2, "end": 1987.68, "word": " لأن", "probability": 0.64892578125}, {"start": 1987.68, "end": 1987.9, "word": " هذا", "probability": 0.7919921875}, {"start": 1987.9, "end": 1988.34, "word": " أكبر", "probability": 0.96826171875}, {"start": 1988.34, "end": 1988.54, "word": " من", "probability": 0.98681640625}, {"start": 1988.54, "end": 1988.76, "word": " ايه", "probability": 0.7786458333333334}, {"start": 1988.76, "end": 1988.88, "word": " و", "probability": 0.736328125}, {"start": 1988.88, "end": 1989.1, "word": " أصار", "probability": 0.6571451822916666}, {"start": 1989.1, "end": 1989.38, "word": " زائد", "probability": 0.8043619791666666}, {"start": 1989.38, "end": 1989.56, "word": " واحد", "probability": 0.96728515625}, {"start": 1989.56, "end": 1989.68, "word": " زي", "probability": 0.867919921875}, {"start": 1989.68, "end": 1989.78, "word": " ما", "probability": 0.9345703125}, {"start": 1989.78, "end": 1990.02, "word": " عملنا", "probability": 0.9534505208333334}, {"start": 1990.02, "end": 1990.42, "word": " فوق", "probability": 0.83740234375}, {"start": 1990.42, "end": 1991.02, "word": " اللي", "probability": 0.94873046875}, {"start": 1991.02, "end": 1991.14, "word": " هو", "probability": 0.97509765625}, {"start": 1991.14, "end": 1991.4, "word": " أكبر", "probability": 0.9765625}, {"start": 1991.4, "end": 1991.74, "word": " strictly", "probability": 0.436279296875}, {"start": 1991.74, "end": 1992.02, "word": " من", "probability": 0.98828125}, {"start": 1992.02, "end": 1992.44, "word": " مين", "probability": 0.9638671875}, {"start": 1992.44, "end": 1993.12, "word": " من", "probability": 0.91796875}, {"start": 1993.12, "end": 1993.7, "word": " واحد", "probability": 0.994140625}, {"start": 1993.7, "end": 1994.06, "word": " إذا", "probability": 0.81396484375}, {"start": 1994.06, "end": 1994.38, "word": " صار", "probability": 0.833740234375}, {"start": 1994.38, "end": 1994.56, "word": " هذا", "probability": 0.9716796875}, {"start": 1994.56, "end": 1994.92, "word": " أكبر", "probability": 0.9752604166666666}, {"start": 1994.92, "end": 1995.06, "word": " من", "probability": 0.994140625}, {"start": 1995.06, "end": 1995.32, "word": " واحد", "probability": 0.99365234375}, {"start": 1995.32, "end": 1995.42, "word": " و", "probability": 0.72998046875}, {"start": 1995.42, "end": 1995.58, "word": " هذا", "probability": 0.9365234375}, {"start": 1995.58, "end": 1995.82, "word": " أكبر", "probability": 0.9637044270833334}, {"start": 1995.82, "end": 1996.0, "word": " من", "probability": 0.990234375}, {"start": 1996.0, "end": 1996.46, "word": " واحد", "probability": 0.993408203125}, {"start": 1996.46, "end": 1997.42, "word": " و", "probability": 0.89208984375}, {"start": 1997.42, "end": 1997.72, "word": " هذا", "probability": 0.91943359375}, {"start": 1997.72, "end": 1998.28, "word": " prime", "probability": 0.62646484375}, {"start": 1998.28, "end": 1998.98, "word": " إذا", "probability": 0.95654296875}, {"start": 1998.98, "end": 1999.24, "word": " صار", "probability": 0.9677734375}, {"start": 1999.24, "end": 1999.84, "word": " contradiction", "probability": 0.8779296875}, {"start": 1999.84, "end": 2001.6, "word": " واضح", "probability": 0.8518880208333334}, {"start": 2001.6, "end": 2003.34, "word": " therefore", "probability": 0.44580078125}, {"start": 2003.34, "end": 2004.12, "word": " K", "probability": 0.50390625}], "temperature": 1.0}, {"id": 78, "seek": 203501, "start": 2005.59, "end": 2035.01, "text": "Can't be positive يعني K is a prime يعني إن اللي ما بتقولك أو اللي وصلنا إله لما الـ A K minus واحد is prime والـ A أكبر من سفر والـ K أكبر سوا اتنين لازم يطلع عند الـ A بسوا اتنين والـ K نفسهاش is prime أي سؤال طيب يا شباب", "tokens": [11531, 380, 312, 3353, 37495, 22653, 591, 307, 257, 5835, 37495, 22653, 36145, 13672, 1829, 19446, 39894, 39648, 4117, 34051, 13672, 1829, 4032, 36520, 8315, 11933, 43761, 5296, 15042, 2423, 39184, 316, 591, 3175, 36764, 24401, 307, 5835, 16070, 39184, 316, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 16070, 39184, 591, 5551, 4117, 26890, 8608, 14407, 1975, 2655, 1863, 9957, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 43242, 2423, 39184, 316, 4724, 3794, 14407, 1975, 2655, 1863, 9957, 16070, 39184, 591, 8717, 36178, 3224, 33599, 307, 5835, 36632, 8608, 33604, 6027, 23032, 1829, 3555, 35186, 13412, 3555, 16758], "avg_logprob": -0.23595328463448417, "compression_ratio": 1.6878048780487804, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2005.59, "end": 2005.99, "word": "Can't", "probability": 0.61376953125}, {"start": 2005.99, "end": 2006.15, "word": " be", "probability": 0.8759765625}, {"start": 2006.15, "end": 2006.77, "word": " positive", "probability": 0.8984375}, {"start": 2006.77, "end": 2007.17, "word": " يعني", "probability": 0.927978515625}, {"start": 2007.17, "end": 2007.65, "word": " K", "probability": 0.228759765625}, {"start": 2007.65, "end": 2009.13, "word": " is", "probability": 0.87548828125}, {"start": 2009.13, "end": 2009.55, "word": " a", "probability": 0.44677734375}, {"start": 2009.55, "end": 2009.85, "word": " prime", "probability": 0.76806640625}, {"start": 2009.85, "end": 2010.49, "word": " يعني", "probability": 0.891845703125}, {"start": 2010.49, "end": 2011.43, "word": " إن", "probability": 0.19873046875}, {"start": 2011.43, "end": 2011.89, "word": " اللي", "probability": 0.78759765625}, {"start": 2011.89, "end": 2012.05, "word": " ما", "probability": 0.32080078125}, {"start": 2012.05, "end": 2012.87, "word": " بتقولك", "probability": 0.9430338541666666}, {"start": 2012.87, "end": 2013.83, "word": " أو", "probability": 0.900390625}, {"start": 2013.83, "end": 2013.99, "word": " اللي", "probability": 0.98486328125}, {"start": 2013.99, "end": 2014.37, "word": " وصلنا", "probability": 0.98095703125}, {"start": 2014.37, "end": 2014.71, "word": " إله", "probability": 0.603271484375}, {"start": 2014.71, "end": 2015.09, "word": " لما", "probability": 0.87353515625}, {"start": 2015.09, "end": 2015.25, "word": " الـ", "probability": 0.5084228515625}, {"start": 2015.25, "end": 2015.31, "word": " A", "probability": 0.314208984375}, {"start": 2015.31, "end": 2015.47, "word": " K", "probability": 0.7392578125}, {"start": 2015.47, "end": 2015.77, "word": " minus", "probability": 0.371826171875}, {"start": 2015.77, "end": 2016.03, "word": " واحد", "probability": 0.93896484375}, {"start": 2016.03, "end": 2016.17, "word": " is", "probability": 0.951171875}, {"start": 2016.17, "end": 2016.65, "word": " prime", "probability": 0.54248046875}, {"start": 2016.65, "end": 2017.43, "word": " والـ", "probability": 0.641357421875}, {"start": 2017.43, "end": 2017.51, "word": " A", "probability": 0.83544921875}, {"start": 2017.51, "end": 2017.79, "word": " أكبر", "probability": 0.970703125}, {"start": 2017.79, "end": 2017.95, "word": " من", "probability": 0.98291015625}, {"start": 2017.95, "end": 2018.27, "word": " سفر", "probability": 0.7122395833333334}, {"start": 2018.27, "end": 2018.43, "word": " والـ", "probability": 0.705810546875}, {"start": 2018.43, "end": 2018.53, "word": " K", "probability": 0.86376953125}, {"start": 2018.53, "end": 2018.73, "word": " أكبر", "probability": 0.9856770833333334}, {"start": 2018.73, "end": 2018.95, "word": " سوا", "probability": 0.453125}, {"start": 2018.95, "end": 2019.35, "word": " اتنين", "probability": 0.9200439453125}, {"start": 2019.35, "end": 2020.11, "word": " لازم", "probability": 0.9869791666666666}, {"start": 2020.11, "end": 2020.37, "word": " يطلع", "probability": 0.988037109375}, {"start": 2020.37, "end": 2020.55, "word": " عند", "probability": 0.82666015625}, {"start": 2020.55, "end": 2020.69, "word": " الـ", "probability": 0.74853515625}, {"start": 2020.69, "end": 2020.81, "word": " A", "probability": 0.9189453125}, {"start": 2020.81, "end": 2021.15, "word": " بسوا", "probability": 0.76611328125}, {"start": 2021.15, "end": 2021.73, "word": " اتنين", "probability": 0.97802734375}, {"start": 2021.73, "end": 2022.55, "word": " والـ", "probability": 0.76953125}, {"start": 2022.55, "end": 2022.75, "word": " K", "probability": 0.91650390625}, {"start": 2022.75, "end": 2024.15, "word": " نفسهاش", "probability": 0.73590087890625}, {"start": 2024.15, "end": 2025.07, "word": " is", "probability": 0.90185546875}, {"start": 2025.07, "end": 2025.45, "word": " prime", "probability": 0.8994140625}, {"start": 2025.45, "end": 2026.69, "word": " أي", "probability": 0.71337890625}, {"start": 2026.69, "end": 2027.27, "word": " سؤال", "probability": 0.9959309895833334}, {"start": 2027.27, "end": 2034.63, "word": " طيب", "probability": 0.9075520833333334}, {"start": 2034.63, "end": 2034.75, "word": " يا", "probability": 0.986328125}, {"start": 2034.75, "end": 2035.01, "word": " شباب", "probability": 0.9928385416666666}], "temperature": 1.0}, {"id": 79, "seek": 205767, "start": 2037.82, "end": 2057.68, "text": "نجي لآخر نظرية في الـ Section اللي هي theorem 11-2 بتقولّي أن an even perfect number an ends in the digits 6 or 8 بيقولّي أن اللي هو الـ even perfect number", "tokens": [1863, 7435, 1829, 5296, 148, 95, 34740, 8717, 19913, 2288, 10632, 8978, 2423, 39184, 1100, 882, 13672, 1829, 39896, 20904, 2975, 12, 17, 39894, 39648, 11703, 1829, 14739, 364, 754, 2176, 1230, 364, 5314, 294, 264, 27011, 1386, 420, 1649, 4724, 1829, 39648, 11703, 1829, 14739, 13672, 1829, 31439, 2423, 39184, 754, 2176, 1230], "avg_logprob": -0.37471591342579236, "compression_ratio": 1.355263157894737, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2037.82, "end": 2038.2, "word": "نجي", "probability": 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0.452880859375}, {"start": 2045.06, "end": 2045.66, "word": " an", "probability": 0.11480712890625}, {"start": 2045.66, "end": 2046.3, "word": " even", "probability": 0.89013671875}, {"start": 2046.3, "end": 2047.08, "word": " perfect", "probability": 0.77392578125}, {"start": 2047.08, "end": 2047.78, "word": " number", "probability": 0.97802734375}, {"start": 2047.78, "end": 2048.22, "word": " an", "probability": 0.505859375}, {"start": 2048.22, "end": 2049.92, "word": " ends", "probability": 0.63525390625}, {"start": 2049.92, "end": 2050.66, "word": " in", "probability": 0.9560546875}, {"start": 2050.66, "end": 2050.9, "word": " the", "probability": 0.86181640625}, {"start": 2050.9, "end": 2051.48, "word": " digits", "probability": 0.9384765625}, {"start": 2051.48, "end": 2052.4, "word": " 6", "probability": 0.74658203125}, {"start": 2052.4, "end": 2053.04, "word": " or", "probability": 0.90283203125}, {"start": 2053.04, "end": 2053.66, "word": " 8", "probability": 0.98095703125}, {"start": 2053.66, "end": 2055.24, "word": " بيقولّي", "probability": 0.779931640625}, {"start": 2055.24, "end": 2055.54, "word": " أن", "probability": 0.70458984375}, {"start": 2055.54, "end": 2055.96, "word": " اللي", "probability": 0.782958984375}, {"start": 2055.96, "end": 2056.18, "word": " هو", "probability": 0.986328125}, {"start": 2056.18, "end": 2056.36, "word": " الـ", "probability": 0.681640625}, {"start": 2056.36, "end": 2056.56, "word": " even", "probability": 0.76220703125}, {"start": 2056.56, "end": 2057.04, "word": " perfect", "probability": 0.900390625}, {"start": 2057.04, "end": 2057.68, "word": " number", "probability": 0.982421875}], "temperature": 1.0}, {"id": 80, "seek": 208196, "start": 2058.77, "end": 2081.97, "text": "أخر اللي هو digit فيه يا ستة يا تمانية يعني خانة العشرات خانة الأحد يا ستة يا تمانية يعني بمعنى أخر حيكون عنده الأن يا بطابق الستة مضله عشرة يا بطابق التمانية ايش مضله عشرة واضح؟ إذا بدنا الآن نثبت ما يليه", "tokens": [10721, 34740, 13672, 1829, 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"end": 2078.93, "word": " الآن", "probability": 0.81201171875}, {"start": 2078.93, "end": 2080.71, "word": " نثبت", "probability": 0.990966796875}, {"start": 2080.71, "end": 2081.03, "word": " ما", "probability": 0.93603515625}, {"start": 2081.03, "end": 2081.97, "word": " يليه", "probability": 0.6410319010416666}], "temperature": 1.0}, {"id": 81, "seek": 211937, "start": 2090.91, "end": 2119.37, "text": "Theorem Theorem 11-2 if n is an even perfect number then n is congruent to 6 modulo 10 or n is congruent to 8 modulo 10 proof", "tokens": [2278, 37956, 440, 37956, 2975, 12, 17, 498, 297, 307, 364, 754, 2176, 1230, 550, 297, 307, 8882, 19226, 281, 1386, 1072, 13455, 1266, 420, 297, 307, 8882, 19226, 281, 1649, 1072, 13455, 1266, 8177], "avg_logprob": -0.2727864724066522, "compression_ratio": 1.358695652173913, "no_speech_prob": 0.0, "words": [{"start": 2090.91, "end": 2092.29, "word": "Theorem", "probability": 0.6087646484375}, {"start": 2092.29, "end": 2093.67, "word": " Theorem", "probability": 0.5716552734375}, {"start": 2093.67, "end": 2095.65, "word": " 11", "probability": 0.50341796875}, {"start": 2095.65, "end": 2096.35, "word": "-2", "probability": 0.71142578125}, {"start": 2096.35, "end": 2098.11, "word": " if", "probability": 0.27099609375}, {"start": 2098.11, "end": 2099.55, "word": " n", "probability": 0.552734375}, {"start": 2099.55, "end": 2100.23, "word": " is", "probability": 0.953125}, {"start": 2100.23, "end": 2101.09, "word": " an", "probability": 0.8720703125}, {"start": 2101.09, "end": 2101.85, "word": " even", "probability": 0.89453125}, {"start": 2101.85, "end": 2104.01, "word": " perfect", "probability": 0.716796875}, {"start": 2104.01, "end": 2106.45, "word": " number", "probability": 0.96533203125}, {"start": 2106.45, "end": 2108.69, "word": " then", "probability": 0.671875}, {"start": 2108.69, "end": 2110.11, "word": " n", "probability": 0.88427734375}, {"start": 2110.11, "end": 2110.63, "word": " is", "probability": 0.927734375}, {"start": 2110.63, "end": 2111.29, "word": " congruent", "probability": 0.97705078125}, {"start": 2111.29, "end": 2111.51, "word": " to", "probability": 0.76904296875}, {"start": 2111.51, "end": 2112.17, "word": " 6", "probability": 0.9267578125}, {"start": 2112.17, "end": 2112.63, "word": " modulo", "probability": 0.682861328125}, {"start": 2112.63, "end": 2113.01, "word": " 10", "probability": 0.95849609375}, {"start": 2113.01, "end": 2114.21, "word": " or", "probability": 0.87451171875}, {"start": 2114.21, "end": 2114.75, "word": " n", "probability": 0.96142578125}, {"start": 2114.75, "end": 2115.25, "word": " is", "probability": 0.94580078125}, {"start": 2115.25, "end": 2115.75, "word": " congruent", "probability": 0.966796875}, {"start": 2115.75, "end": 2115.95, "word": " to", "probability": 0.9794921875}, {"start": 2115.95, "end": 2116.35, "word": " 8", "probability": 0.97900390625}, {"start": 2116.35, "end": 2117.61, "word": " modulo", "probability": 0.939453125}, {"start": 2117.61, "end": 2118.11, "word": " 10", "probability": 0.9560546875}, {"start": 2118.11, "end": 2119.37, "word": " proof", "probability": 0.487548828125}], "temperature": 1.0}, {"id": 82, "seek": 215182, "start": 2127.12, "end": 2151.82, "text": "suppose suppose that n is even perfect number then it can be written as then it can be written as n بيساوى اتنين أس كي ماينس واحد فتنين أس كي ناقص واحد where", "tokens": [36622, 541, 7297, 300, 297, 307, 754, 2176, 1230, 550, 309, 393, 312, 3720, 382, 550, 309, 393, 312, 3720, 382, 297, 4724, 1829, 3794, 995, 2407, 7578, 1975, 2655, 1863, 9957, 5551, 3794, 9122, 1829, 19446, 9957, 3794, 36764, 24401, 6156, 2655, 1863, 9957, 5551, 3794, 9122, 1829, 8717, 995, 4587, 9381, 36764, 24401, 689], "avg_logprob": -0.286732460323133, "compression_ratio": 1.5114503816793894, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2127.12, "end": 2128.16, "word": "suppose", "probability": 0.59136962890625}, {"start": 2128.16, "end": 2129.2, "word": 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0.9736328125}, {"start": 2142.82, "end": 2144.2, "word": " then", "probability": 0.5712890625}, {"start": 2144.2, "end": 2144.48, "word": " it", "probability": 0.9775390625}, {"start": 2144.48, "end": 2144.7, "word": " can", "probability": 0.95703125}, {"start": 2144.7, "end": 2144.86, "word": " be", "probability": 0.9462890625}, {"start": 2144.86, "end": 2145.1, "word": " written", "probability": 0.9248046875}, {"start": 2145.1, "end": 2145.52, "word": " as", "probability": 0.97607421875}, {"start": 2145.52, "end": 2145.96, "word": " n", "probability": 0.65185546875}, {"start": 2145.96, "end": 2147.46, "word": " بيساوى", "probability": 0.5917561848958334}, {"start": 2147.46, "end": 2147.78, "word": " اتنين", "probability": 0.744171142578125}, {"start": 2147.78, "end": 2147.98, "word": " أس", "probability": 0.5499267578125}, {"start": 2147.98, "end": 2148.2, "word": " كي", "probability": 0.684814453125}, {"start": 2148.2, "end": 2148.54, "word": " ماينس", "probability": 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2180.75, "end": 2181.11, "word": " مرة", "probability": 0.994384765625}, {"start": 2181.11, "end": 2182.73, "word": " وهي", "probability": 0.44183349609375}, {"start": 2182.73, "end": 2183.09, "word": " مفتاح", "probability": 0.9920654296875}, {"start": 2183.09, "end": 2183.45, "word": " الحل", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 84, "seek": 221238, "start": 2184.42, "end": 2212.38, "text": "نفترض أن الـ N هو even perfect number مدام even perfect number إذا حسب النظرية الأولى إيش هتطلع الـ N تبعتنا على الصورة اللي أمامنا؟ وهيكون هذا إيش ماله؟ إي برايم زي ما أثبتنا في النظرية الأولى لأن في اللمّة مدام تهدي برايم وعندي K أكبر وساوي 2 إذا نحسب اللمّة هذه هتطلع الكياش برضه إي برايم أي سؤال؟ مدام الـ K برايم", "tokens": [1863, 5172, 2655, 43042, 14739, 2423, 39184, 426, 31439, 754, 2176, 1230, 3714, 3215, 10943, 754, 2176, 1230, 11933, 15730, 11331, 35457, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 11933, 1829, 8592, 8032, 2655, 9566, 1211, 3615, 2423, 39184, 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"temperature": 1.0}, {"id": 94, "seek": 249653, "start": 2467.09, "end": 2496.53, "text": "إذا هذه بالطابق 2 وهذه بالنسبة 16 بالنسبة للعشرة جديش 6 أُس 2 أما برضه بيبقى أشمالها اللي هو في 6 ماقص 6 بيساوي 12 ماقص 6 اللي هي بالطابق 6 modulo 10 واضحة أه نيجي للي بعدها case 2 case 2", "tokens": [28814, 15730, 29538, 20666, 9566, 16758, 4587, 568, 37037, 24192, 20666, 1863, 35457, 3660, 3165, 20666, 1863, 35457, 3660, 24976, 3615, 8592, 25720, 10874, 16254, 8592, 1386, 5551, 10859, 3794, 568, 5551, 15042, 4724, 43042, 3224, 4724, 1829, 3555, 4587, 7578, 5551, 8592, 2304, 6027, 11296, 13672, 1829, 31439, 8978, 1386, 19446, 4587, 9381, 1386, 4724, 1829, 3794, 995, 45865, 2272, 19446, 4587, 9381, 1386, 13672, 1829, 39896, 20666, 9566, 16758, 4587, 1386, 1072, 13455, 1266, 4032, 46958, 5016, 3660, 5551, 3224, 8717, 1829, 7435, 1829, 5296, 20292, 39182, 11296, 1389, 568, 1389, 568], "avg_logprob": -0.373026304495962, "compression_ratio": 1.6795580110497237, "no_speech_prob": 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