Question, what are the chances for obtaining the same, prime factor 55049? The SUM of List A gives a factor of 17 x 55049 and the sum of list B gives a factor of 19 x 55049
I want to understand how to quantify the probability of attaining the same prime factor of two randomly generated number series, in two seperate lists. The lists are independent of each other. The sum of two lists, gives a number with a prime factor. How do i quantify the probability for the prime factor to be the same. In this case I generated two list which is randomly produced, by numpy, uniform distribution.
The numbers in list A is produced, by uniform distrubtion with added noise of about 1, the probability distribution is uniform. https://docs.scipy.org/doc/numpy-1.13.0/reference/generated/numpy.random.uniform.html#numpy.random.uniform
Next for list B, all the random numbers is produced by a predetermined multiple of 19. The numerical values shifts sometimes with 1000's and 100. And is always a factor of 19. The number 19 is multiplied by a random number, with numpy random generator, how this time it is sampled by uniform distribution,
So programming wise it would look something like random.randint(1,200) = X
X * 19 = entries in B.
Now you know how both numbers in both list, A and B is generated.
The SUM of List A gives a factor of 17 x 55049 and the sum of list B gives a factor of 19 x 55049
What are the probability for attaining the same factor, of 55049? 55049 is also a prime, 17, 19 with twin-primes.
For both randomly picked integers it is, 1/pA * 1/pB = 1/p where pA=pB
How do I take into consideration the series distribution of numbers, list A and B giving this factor? Given the fact from the list A is produced entirely by random generator, along with list B, however with a preconditioned prime factor of 19.
A = [5, 11, 24, 58, 106, 123, 243, 244, 249, 292, 293, 306, 321, 336, 354, 374, 417, 421, 496, 532, 545, 566, 583, 587, 641, 659, 675, 711, 728, 744, 749, 757, 784, 810, 833, 869, 879, 929, 978, 1016, 1019, 1047, 1050, 1055, 1077, 1099, 1102, 1117, 1156, 1167, 1177, 1220, 1244, 1249, 1254, 1255, 1272, 1288, 1326, 1338, 1348, 1394, 1430, 1439, 1440, 1446, 1484, 1486, 1573, 1591, 1621, 1622, 1635, 1636, 1646, 1748, 1752, 1762, 1766, 1788, 1820, 1839, 1848, 1852, 1874, 1897, 1934, 1941, 1950, 1969, 1970, 1979, 2018, 2081, 2085, 2147, 2176, 2202, 2203, 2252, 2257, 2285, 2300, 2316, 2319, 2320, 2322, 2332, 2345, 2400, 2406, 2425, 2428, 2466, 2473, 2507, 2528, 2532, 2551, 2561, 2571, 2602, 2603, 2610, 2614, 2657, 2665, 2717, 2747, 2752, 2767, 2807, 2811, 2816, 2818, 2825, 2846, 2862, 2896, 2913, 2952, 2961, 3005, 3020, 3022, 3027, 3047, 3087, 3113, 3119, 3138, 3171, 3220, 3255, 3270, 3285, 3426, 3433, 3465, 3491, 3509, 3522, 3531, 3544, 3563, 3641, 3651, 3694, 3698, 3714, 3715, 3728, 3743, 3761, 3763, 3780, 3824, 3828, 3841, 3852, 3862, 3874, 3904, 3916, 3948, 3971, 4008, 4050, 4109, 4122, 4154, 4158, 4167, 4183, 4192, 4193, 4209, 4215, 4238, 4259, 4268, 4307, 4328, 4330, 4347, 4365, 4382, 4398, 4418, 4463, 4480, 4522, 4527, 4618, 4632, 4672, 4676, 4699, 4739, 4762, 4775, 4784, 4788, 4844, 4888, 4890, 4896, 4906, 4907, 4913, 4928, 4957, 4993, 4998, 5015, 5052, 5084, 5106, 5135, 5167, 5174, 5207, 5227, 5230, 5272, 5308, 5317, 5324, 5353, 5395, 5408, 5460, 5464, 5509, 5536, 5565, 5594, 5597, 5602, 5616, 5638, 5648, 5658, 5664, 5690, 5692, 5710, 5716, 5753, 5763, 5793, 5854, 5863, 5874, 5880, 5895, 5903, 5939, 5945, 5947, 5963, 5990, 6033, 6037, 6043, 6064, 6087, 6125, 6130, 6149, 6161, 6189, 6195, 6208]
B = [836, 2641, 7809, 5871, 1938, 4541, 8189, 11894, 2261, 6042, 12863, 8018, 7923, 1995, 5510, 13148, 3743, 3439, 8778, 3116, 2394, 4826, 8569, 14915, 2280, 1938, 16074, 7923, 3363, 6954, 6650, 2679, 4104, 5206, 7999, 6517, 3515, 7030, 4712, 3211, 3762, 5035, 6270, 5643, 6289, 7391, 6897, 10241, 3021, 7334, 5358, 8816, 3040, 3838, 5092, 3477, 5377, 2527, 7448, 4351, 5130, 3857, 6973, 4104, 1900, 1463, 3743, 6289, 1976, 2261, 4009, 4180, 2660, 5719, 3553, 3477, 4332, 4294, 836, 4598, 2052, 1653, 931, 1767, 1482, 836, 7809, 2090, 3059, 4104, 8436, 4560, 1615, 3914, 4085, 1976, 3496, 3990, 7448, 2109, 2679, 4636, 1615, 2527, 2603, 1843, 4579, 2109, 1045, 2375, 3572, 5339, 2090, 1425, 2375, 8265, 3534, 3933, 2109, 5358, 2983, 2204, 2698, 7942, 6517, 2033, 4750, 7049, 2489, 3857, 2204, 5795, 2546, 1843, 9443, 5358, 13281, 3648, 5206, 3762, 2489, 4123, 1406, 513, 1273, 342, 1197, 2375, 1786, 1691, 855, 6441, 4921, 1767, 7144, 3059, 1520, 5757, 6783, 2831, 2698, 2755, 2698, 1254, 5472, 2128, 5681, 4104, 4484, 3363, 3325, 7315, 3686, 2052, 817, 2318, 2166, 1026, 3135, 2071, 1026, 950, 1767, 1026, 1026, 2926, 1615, 1653, 3819, 2413, 9576, 4446, 7980, 4332, 2166, 5016, 3002, 9025, 2622, 2831, 12046, 1957, 1691, 3591, 1919, 3059, 3116, 1634, 855, 1748, 779, 6460, 8360, 4142, 3040, 2223, 3040, 2527, 836, 1520, 3002, 665, 152, 1805, 4864, 1254, 817, 931, 798, 1330, 1463, 2318, 1159, 627, 513, 2375, 5396, 6422, 6593, 2546, 4902, 3249, 4256, 6726, 1425, 1368, 3002, 931, 2432, 1425, 1805, 2793, 4237, 950, 494, 836, 1178, 1843, 3363, 1615, 304, 475, 2394, 969, 2242, 1558, 2831, 836, 323, 1653, 76, 817, 1425, 3439, 2109, 1026, 1045, 779, 133, 76, 1444, 874, 228, 2090, 551, 361, 1292, 1349, 1026, 1862, 1995, 2223, 1349, 1330]
What I am looking for is if there is a theoritical way to quantify the probability for attaining the same prime factor of two randomly generated lists.
The bounds for list A, is (1, 141) random numbers, for list B, X is (4, 846) random int numbers. Using np.random.randint(a,b), python
I was tipped to look at the birthday paradox. It makes sense the greater pool size of numbers, to pick from, the chances for gaining the same prime factor is greater. But this expirement relates to comparing to sums to each other. Confined to this expirement only. And according to this paradox, the chances of that, is practically , zero near n=2.
Check this link out. I hope it will give you some idea on the code you are working on.