def testFactorial() -> bool:
sample = [
[0, 1],
[1, 1],
[2, 2],
[3, 6],
[4, 24],
[5, 120],
[6, 720],
[7, 5040],
[8, 40320],
[9, 362880],
[10, 3_628_800],
[11, 39_916_800],
[12, 479_001_600],
]
for i, _ in enumerate(sample):
if NumberTheory.factorial(sample[i][0]) != sample[i][1]:
return False
return True
def testIsPrime() -> bool:
sample = [
[0, 1],
[1, 1],
[2, 2],
[3, 2],
[4, 4],
[5, 2],
[6, 4],
[7, 2],
[8, 4],
[9, 4],
[10, 4],
[11, 2],
[12, 4],
[13, 2],
[14, 4],
[15, 4],
[16, 4],
[17, 2],
[18, 4],
[19, 2],
[20, 4],
[21, 4],
[22, 4],
[23, 2],
[24, 4],
[25, 4],
[26, 4],
[27, 4],
[28, 4],
[29, 2],
[30, 4],
[31, 2],
[32, 4],
[33, 4],
[34, 4],
[35, 4],
[36, 4],
[37, 2],
[38, 4],
[39, 4],
[40, 4],
[41, 2],
[42, 4],
[43, 2],
[44, 4],
[45, 4],
[46, 4],
[47, 2],
[48, 4],
[49, 4],
[50, 4],
[51, 4],
[52, 4],
[53, 2],
[54, 4],
[55, 4],
[56, 4],
[57, 4],
[58, 4],
[59, 2],
[60, 4],
[61, 2],
[62, 4],
[63, 4],
[64, 4],
[65, 4],
[66, 4],
[67, 2],
[68, 4],
[69, 4],
[70, 4],
[71, 2],
[72, 4],
[73, 2],
[74, 4],
[75, 4],
[76, 4],
[77, 4],
[78, 4],
[79, 2],
[80, 4],
[81, 4],
[82, 4],
[83, 2],
[84, 4],
[85, 4],
[86, 4],
[87, 4],
[88, 4],
[89, 2],
[90, 4],
[91, 4],
[92, 4],
[93, 4],
[94, 4],
[95, 4],
[96, 4],
[97, 2],
[98, 4],
[99, 4],
[100, 4],
[101, 2],
[102, 4],
[103, 2],
[104, 4],
[105, 4],
[106, 4],
[107, 2],
[108, 4],
[109, 2],
[110, 4],
[111, 4],
[112, 4],
[113, 2],
[114, 4],
[115, 4],
[116, 4],
[117, 4],
[118, 4],
[119, 4],
[120, 4],
[121, 4],
[122, 4],
[123, 4],
[124, 4],
[125, 4],
[126, 4],
[127, 2],
[170, 4],
[271, 2],
[357, 4],
[225, 4],
[440, 4],
[235, 4],
[274, 4],
[383, 2],
[313, 2],
[434, 4],
[222, 4],
[137, 2],
[155, 4],
[465, 4],
[249, 4],
[141, 4],
[5307, 4],
[6374, 4],
[951, 4],
[7236, 4],
[2027, 2],
[2382, 4],
[2251, 2],
[757, 2],
[6678, 4],
[3206, 4],
[6257, 2],
[615, 4],
[1677, 4],
[2086, 4],
[4158, 4],
[4723, 2],
[7755, 4],
[1583, 2],
[6547, 2],
[4219, 2],
[660, 4],
[7698, 4],
[3121, 2],
[3881, 2],
[2541, 4],
[4696, 4],
[4091, 2],
[5222, 4],
[4021, 2],
[5839, 2],
[6048, 4],
[5521, 2],
[47908, 4],
[35060, 4],
[47361, 4],
[48859, 2],
[56067, 4],
[70451, 2],
[9735, 4],
[19763, 2],
[97943, 2],
[9933, 4],
[61651, 2],
[11407, 4],
[8774, 4],
[48383, 2],
[51001, 2],
[73029, 4],
[27690, 4],
[30466, 4],
[71479, 2],
[84701, 2],
[28643, 2],
[57075, 4],
[99745, 4],
[100921, 4],
[40496, 4],
[9798, 4],
[41603, 2],
[46912, 4],
[49852, 4],
[55871, 2],
[10993, 2],
[79657, 2],
[609680, 4],
[180540, 4],
[147672, 4],
[819031, 2],
[149623, 2],
[1_056_048, 4],
[483389, 2],
[452831, 2],
[415109, 2],
[185021, 2],
[715823, 2],
[744081, 4],
[1_276_157, 2],
[192978, 4],
[631537, 2],
[554226, 4],
[653111, 2],
[607346, 4],
[452539, 2],
[815939, 2],
[247199, 4],
[1_245_953, 2],
[974803, 2],
[185813, 2],
[1_261_831, 2],
[443227, 2],
[1_057_294, 4],
[427241, 2],
[627391, 2],
[1_019_663, 2],
[629142, 4],
[164503, 2],
[6_006_421, 2],
[9_499_199, 2],
[12_598_247, 2],
[13_919_909, 2],
[8_975_950, 4],
[6_655_578, 4],
[2_388_697, 2],
[14_018_237, 4],
[7_871_261, 2],
[1_678_013, 2],
[2_654_027, 2],
[10_142_801, 2],
[2_291_487, 4],
[3_893_849, 2],
[1_308_913, 4],
[14_162_880, 4],
]
for i, _ in enumerate(sample):
if sample[i][1] == 1:
if NumberTheory.isPrime(sample[i][0]):
return False
elif sample[i][1] == 2:
if not NumberTheory.isPrime(sample[i][0]):
return False
else:
if NumberTheory.isPrime(sample[i][0]):
return False
return True
def testIsOdd() -> bool:
sample = [
[0, 0],
[1, 1],
[-1, 1],
[60, 0],
[62, 0],
[42, 0],
[-87, 1],
[-98, 0],
[-56, 0],
[41, 1],
[14, 0],
[20, 0],
[-63, 1],
[-81, 1],
[-39, 1],
[33, 1],
[-32, 0],
[-50, 0],
[-1471, 1],
[4046, 0],
[5019, 1],
[4521, 1],
[-8744, 0],
[4787, 1],
[4973, 1],
[-1184, 0],
[-4437, 1],
[-5871, 1],
[-4298, 0],
[-2027, 1],
[-2796, 0],
[-2209, 1],
[-6094, 0],
[3257, 1],
[-4732, 0],
[7495, 1],
[-3916, 0],
[1469, 1],
[6164, 0],
[-7545, 1],
[-7763, 1],
[7523, 1],
[-8076, 0],
[-3778, 0],
[-1648, 0],
[4220, 0],
[-8551, 1],
[9692, 0],
[5394, 0],
[2472, 0],
[4056, 0],
[5769, 1],
[-2322, 0],
[503, 1],
[-8721, 1],
[-6344, 0],
[-4335, 1],
[1677, 1],
[-1703, 1],
[-4086, 0],
[7076, 0],
[-7165, 1],
[7636, 0],
[-8043, 1],
[-3753, 1],
[4007, 1],
[-261, 1],
[-6538, 0],
[9766, 0],
[-7563, 1],
[-7944, 0],
[8922, 0],
[-5759, 1],
[-8791, 1],
[-2211, 1],
[3493, 1],
[5573, 1],
[-2645, 1],
[-603656, 0],
[807727, 1],
[-69847, 1],
[-843676, 0],
[-830961, 1],
[-608772, 0],
[931043, 1],
[855512, 0],
[358482, 0],
[-98919, 1],
[215211, 1],
[-933334, 0],
[-613634, 0],
[-95643, 1],
[53934, 0],
[161818, 0],
[67_041_621, 1],
[99_662_694, 0],
[-94_392_019, 1],
[-20_543_495, 1],
[-27_591_794, 0],
[-8_314_396, 0],
[97_455_764, 0],
[59_367_920, 0],
[26_856_309, 1],
[64_178_815, 1],
[-11_480_741, 1],
[45_428_276, 0],
[46_193_175, 1],
[-31_079_636, 0],
[63_115_980, 0],
[42_559_270, 0],
[-1_645_871_504, 0],
[-1_233_918_598, 0],
[722_012_346, 0],
[-1_525_999_934, 0],
[-365_543_955, 1],
[2_008_798_151, 1],
[-1_300_713_468, 0],
[1_425_587_979, 1],
[1_324_445_673, 1],
[2_136_612_365, 1],
[-995_371_213, 1],
[-2_048_365_905, 1],
[2_096_138_065, 1],
[-768_738_192, 0],
[-846_034_014, 0],
[411_817_058, 0],
[2_147_483_647, 1],
[-2_147_483_648, 0],
]
for i, _ in enumerate(sample):
if sample[i][1] == 0:
if NumberTheory.isOdd(sample[i][0]):
return False
else:
if not NumberTheory.isOdd(sample[i][0]):
return False
return True
def testIsCoprime() -> bool:
sample = [
[0, 1, 1],
[1, 0, 1],
[1, 1, 1],
[-1, -1, 1],
[15, -45, 0],
[-7, 51, 1],
[-3, 75, 0],
[-84, -32, 0],
[-21, -71, 1],
[89, -11, 1],
[-40, -9, 1],
[92, 26, 0],
[14, -95, 1],
[5, -99, 1],
[-45, -57, 0],
[59, -97, 1],
[-16, 37, 1],
[97, 49, 1],
[5998, -3871, 1],
[-2152, -2909, 1],
[8823, 629, 0],
[7589, -7035, 1],
[-8669, 6398, 1],
[1059, 3522, 0],
[9892, -2990, 0],
[-1819, 4740, 1],
[7900, -7244, 0],
[8072, -1226, 0],
[-6875, 5777, 1],
[-828, 8859, 0],
[-3929, 1143, 1],
[-5397, 1880, 1],
[-9397, -4343, 1],
[2389, -4026, 1],
[-6838, -7802, 0],
[-6118, 7944, 0],
[1408, -8483, 1],
[-507, 3510, 0],
[5030, -4818, 0],
[2563, -1867, 1],
[3317, -4585, 1],
[-2448, -2215, 1],
[-1982, -3811, 1],
[645, 7907, 1],
[5812, 1657, 1],
[3944, -5997, 1],
[-2410, -6522, 0],
[4565, 9055, 0],
[8478, 1099, 0],
[6444, -7298, 0],
[7606, -7006, 0],
[2491, -2017, 1],
[7151, -9724, 1],
[2958, -5697, 0],
[5134, -7701, 0],
[-3544, 9042, 0],
[8826, -4548, 0],
[6794, -5322, 0],
[-6906, 7502, 0],
[172, 8480, 0],
[8244, 4622, 0],
[-7315, 5253, 1],
[7011, 4285, 1],
[-3132, -4999, 1],
[-7332, -655, 1],
[9661, -1750, 1],
[7560, -3128, 0],
[1334, 6234, 0],
[8075, 6450, 0],
[3283, 8980, 1],
[3364, 8482, 0],
[4909, 8302, 1],
[9332, -2523, 1],
[-8515, 5209, 1],
[-1624, 7640, 0],
[-6463, 2562, 1],
[7912, 5868, 0],
[-4825, -2173, 1],
[28876, 30106, 0],
[-929840, 887043, 1],
[684923, -588038, 1],
[-291411, -299801, 1],
[-905447, -402122, 1],
[830872, -223425, 1],
[831033, -753398, 1],
[-575558, 711716, 0],
[-312296, 515492, 0],
[595308, 963205, 0],
[-770718, -388434, 0],
[353889, 330806, 1],
[-174566, 613742, 0],
[-884075, 26687, 1],
[390743, 204874, 1],
[930615, 86524, 1],
[-84_945_524, 15_427_487, 1],
[76_038_602, -89_688_904, 0],
[50_294_214, -65_802_481, 1],
[83_436_075, 44_248_708, 1],
[54_031_677, 92_370_464, 1],
[-6_019_575, -1_302_029, 1],
[86_952_873, -75_470_243, 1],
[-53_215_372, 28_947_490, 0],
[-37_109_442, 75_623_090, 0],
[-11_656_183, 16_147_085, 1],
[86_439_843, -12_134_914, 1],
[-52_977_427, 48_349_835, 1],
[16_234_161, 26_103_566, 1],
[73_756_826, -6_586_797, 1],
[6_836_355, 11_529_043, 1],
[29_864_126, -80_782_077, 1],
[1_646_787_325, 1_961_513_442, 1],
[-1_755_035_190, -1_801_169_490, 0],
[-1_509_018_194, 1_829_751_775, 1],
[-720_160_017, -1_425_309_680, 1],
[1_216_287_038, 1_821_933_798, 0],
[-1_925_479_607, -1_842_455_762, 1],
[-795_996_486, -1_859_155_567, 1],
[-367_280_505, 321_267_794, 1],
[829_304_526, -1_575_808_585, 1],
[1_457_917_042, 1_083_382_210, 0],
[-377_130_535, 1_526_538_188, 1],
[-1_109_347_700, -1_819_333_109, 1],
[-1_740_794_578, 278_770_346, 0],
[448_156_480, -1_008_775_746, 0],
[442_691_160, 1_680_572_092, 0],
[1_241_208_470, -647_438_045, 0],
[2_147_483_647, -561_158_902, 1],
[761_395_308, -2_147_483_647, 1],
]
for i, _ in enumerate(sample):
if sample[i][2] == 0:
if NumberTheory.isCoprime(sample[i][0], sample[i][1]):
return False
else:
if not NumberTheory.isCoprime(sample[i][0], sample[i][1]):
return False
return True
def testLCM() -> bool:
sample = [
[1, 1, 1],
[-1, -1, 1],
[-85, -8, 680],
[33, -2, 66],
[8, 32, 32],
[8, 89, 712],
[16, 78, 624],
[-66, -2, 66],
[-50, -62, 1550],
[12, -25, 300],
[-74, -25, 1850],
[4, 24, 24],
[90, 29, 2610],
[-62, -85, 5270],
[-9, -50, 450],
[90, -59, 5310],
[-8732, -1743, 15_219_876],
[-8329, 8430, 70_213_470],
[3300, -1326, 729300],
[-5969, -523, 3_121_787],
[-7044, -8745, 20_533_260],
[-4683, 2491, 11_665_353],
[9729, 4329, 4_679_649],
[-871, 3189, 2_777_619],
[-1158, -3122, 1_807_638],
[9912, -9910, 49_113_960],
[4924, 5842, 14_383_004],
[3980, -6455, 5_138_180],
[5420, -1507, 8_167_940],
[-1090, 7747, 8_444_230],
[-8008, 7290, 29_189_160],
[-2260, -6189, 13_987_140],
[-962, 9376, 4_509_856],
[-351, 8756, 3_073_356],
[-171, 8401, 1_436_571],
[-3110, -7937, 24_684_070],
[6362, 1928, 6_132_968],
[-8230, 964, 3_966_860],
[-5791, 6186, 35_823_126],
[-4204, 9556, 10_043_356],
[-3338, 6848, 11_429_312],
[-760, 8766, 3_331_080],
[-1958, 4928, 438592],
[-3830, -107, 409810],
[-7809, 9720, 25_301_160],
[7665, 209, 1_601_985],
[-6060, 4881, 9_859_620],
[2346, -9979, 1_377_102],
[7125, -5604, 13_309_500],
[9862, 3015, 29_733_930],
[-1148, 8092, 331772],
[8627, 3929, 33_895_483],
[-5320, 8927, 47_491_640],
[-2301, -8803, 20_255_703],
[6395, -8793, 56_231_235],
[6278, -2847, 244842],
[1623, 3406, 5_527_938],
[-3974, 1259, 5_003_266],
[-4014, -3066, 2_051_154],
[7546, -3833, 28_923_818],
[4058, -4338, 8_801_802],
[5066, 7450, 126650],
[-9458, -5234, 24_751_586],
[4142, 5319, 22_031_298],
[4119, -9963, 13_679_199],
[813, 1892, 1_538_196],
[4375, 9055, 7_923_125],
[388, -4329, 1_679_652],
[3927, 5720, 2_042_040],
[5099, -5563, 28_365_737],
[-4174, 4772, 9_959_164],
[-8829, 6842, 60_408_018],
[9834, 8283, 2_468_334],
[-6028, -2949, 17_776_572],
[2627, -2463, 6_470_301],
[9431, -5198, 49_022_338],
[4553, 6198, 28_219_494],
[1368, -8772, 1_000_008],
[-43336, -36185, 1_568_113_160],
[33606, -19136, 321_542_208],
[-23381, 31250, 730_656_250],
[-22377, -22397, 501_177_669],
[-22766, -10042, 114_308_086],
[-37379, -13431, 502_037_349],
[-23248, -18591, 432_203_568],
[-34910, 37688, 657_844_040],
[-29156, 26259, 765_607_404],
[33346, 19239, 641_543_694],
[-31634, 13587, 429_811_158],
[22300, 14536, 81_038_200],
[-25315, 26148, 661_936_620],
[-21579, -43116, 310_133_388],
[-25141, 37870, 952_089_670],
[23741, 10471, 248_592_011],
[26852, -41498, 557_152_148],
[26627, -21629, 575_915_383],
[-13538, -16865, 228_318_370],
[25331, 31258, 791_796_398],
[33885, 13483, 456_871_455],
[-43671, -16383, 238_487_331],
[-29483, 26616, 784_719_528],
[15792, -11008, 10_864_896],
[23749, 40466, 961_027_034],
[-37432, -42397, 1_587_004_504],
[-46035, -24237, 123_972_255],
[-38120, 10830, 41_283_960],
[-11808, -10396, 30_688_992],
[-15667, -15508, 242_963_836],
[-15336, -35057, 537_634_152],
[31050, -13757, 427_154_850],
[42602, -20701, 881_904_002],
[-20505, 18475, 75_765_975],
[35445, 12527, 444_019_515],
[-20600, -23702, 244_130_600],
[21432, 15715, 336_803_880],
[-24635, 45838, 86_863_010],
[20616, 41256, 35_438_904],
[-40536, 29009, 1_175_908_824],
[-29015, -40786, 1_183_405_790],
[17092, -30650, 261_934_900],
[-44577, 31261, 1_393_521_597],
[-35517, 13916, 494_254_572],
[-22680, 39616, 112_311_360],
[33207, -33473, 1_111_537_911],
[30250, -28845, 174_512_250],
[45203, -23693, 1_070_994_679],
[46340, 46341, 2_147_441_940],
[-46340, -46341, 2_147_441_940],
]
for i, _ in enumerate(sample):
if NumberTheory.lcm(sample[i][0], sample[i][1]) != sample[i][2]:
return False
return True
def testGCD() -> bool:
sample = [
[0, 1, 1],
[1, 0, 1],
[1, 1, 1],
[-1, -1, 1],
[-25, 72, 1],
[-16, -48, 16],
[-56, -54, 2],
[29, -60, 1],
[40, -58, 2],
[-61, 97, 1],
[-81, -99, 9],
[-46, 59, 1],
[59, -55, 1],
[-36, 14, 2],
[-42, 19, 1],
[-22, 44, 22],
[-14, 84, 14],
[-99, 6, 3],
[-7864, 2672, 8],
[8228, 2179, 1],
[-1622, -4471, 1],
[8293, -4881, 1],
[9936, 3701, 1],
[3828, -9134, 2],
[-9055, 934, 1],
[-9427, 2762, 1],
[-9960, 6904, 8],
[-2912, 1062, 2],
[7678, 8016, 2],
[-3919, 5143, 1],
[-5080, -9523, 1],
[8388, -952, 4],
[8996, 2305, 1],
[-6576, 3950, 2],
[887, -6760, 1],
[8148, -8500, 4],
[5170, -3469, 1],
[-7312, 2220, 4],
[-9841, 742, 1],
[3525, 3121, 1],
[-8986, 4466, 2],
[5192, -2843, 1],
[2196, 4569, 3],
[8895, 644, 1],
[7633, -1624, 1],
[9405, -2678, 1],
[-4444, -4640, 4],
[2729, 6047, 1],
[-5458, 5100, 2],
[7727, -2644, 1],
[9825, -3348, 3],
[-7670, 1745, 5],
[-9678, -2111, 1],
[4804, -2588, 4],
[4541, 3146, 1],
[8691, -8489, 1],
[-9432, -9286, 2],
[7370, 2247, 1],
[-6928, 7638, 2],
[-2610, 4698, 522],
[999, -349, 1],
[-1954, 5542, 2],
[7277, 7843, 1],
[-815, 3671, 1],
[-4961, -4919, 1],
[-3079, -2410, 1],
[-1594, 2267, 1],
[5889, -1103, 1],
[-2327, 2864, 179],
[-9761, 2090, 1],
[5879, 976, 1],
[-5212, -6742, 2],
[-1803, 3566, 1],
[8078, -9213, 1],
[6391, 8997, 1],
[-7333, -2185, 1],
[9552, 6474, 6],
[3775, -7699, 1],
[-975165, 693821, 1],
[-283946, -681458, 2],
[393833, -268145, 1],
[93577, -938355, 517],
[201821, -279303, 1],
[288085, -62375, 5],
[98342, 460581, 1],
[875349, -88237, 1],
[-101284, -152553, 1],
[-711500, -228037, 1],
[413727, 811772, 1],
[-286175, -99810, 5],
[959681, 662872, 1],
[-541593, -211585, 1],
[935328, -878838, 6],
[544408, -614262, 2],
[56_791_606, 10_091_252, 2],
[76_184_637, 55_338_231, 3],
[87_827_010, -2_054_112, 6],
[-51_336_665, 47_647_691, 1],
[26_786_890, 3_898_842, 2],
[70_964_172, 27_242_363, 1],
[50_572_364, 24_895_820, 4],
[-10_321_594, 90_477_203, 1],
[-90_182_979, -79_448_469, 3],
[73_849_322, -30_438_170, 2],
[-30_825_301, -45_682_165, 1],
[-29_366_775, 65_070_021, 3],
[19_996_288, -66_270_963, 1],
[-3_388_067, 94_646_426, 1],
[28_009_079, 59_009_075, 1],
[-35_854_012, -13_548_532, 4],
[-1_341_557_375, -1_706_521_640, 5],
[-1_703_927_494, 617_390_757, 1],
[-1_926_730_755, 1_188_983_365, 5],
[533_277_970, -542_110_746, 2],
[1_508_525_543, 869_090_704, 1],
[1_234_248_685, 1_606_411_314, 1],
[-1_698_647_648, -1_816_407_074, 2],
[1_149_345_284, 1_170_749_266, 2],
[-711_810_797, -908_541_229, 1],
[424_509_982, 712_101_099, 1],
[1_996_000_380, -457_046_405, 5],
[943_706_285, -419_105_596, 1],
[-249_463_342, -2_050_490_722, 2],
[-1_981_012_181, -1_584_006_152, 1],
[1_483_217_656, 1_658_473_101, 1],
[-1_069_835_847, 1_308_503_268, 3],
[2_147_483_647, -1_884_119_046, 1],
[645_159_694, -2_147_483_647, 1],
]
for i, _ in enumerate(sample):
if NumberTheory.gcd(sample[i][0], sample[i][1]) != sample[i][2]:
return False
return True
def testFibonacci() -> bool:
sample = [
[-31, 1346269],
[-30, -832040],
[-29, 514229],
[-28, -317811],
[-27, 196418],
[-26, -121393],
[-25, 75025],
[-24, -46368],
[-23, 28657],
[-22, -17711],
[-21, 10946],
[-20, -6765],
[-19, 4181],
[-18, -2584],
[-17, 1597],
[-16, -987],
[-15, 610],
[-14, -377],
[-13, 233],
[-12, -144],
[-11, 89],
[-10, -55],
[-9, 34],
[-8, -21],
[-7, 13],
[-6, -8],
[-5, 5],
[-4, -3],
[-3, 2],
[-2, -1],
[-1, 1],
[0, 0],
[1, 1],
[2, 1],
[3, 2],
[4, 3],
[5, 5],
[6, 8],
[7, 13],
[8, 21],
[9, 34],
[10, 55],
[11, 89],
[12, 144],
[13, 233],
[14, 377],
[15, 610],
[16, 987],
[17, 1597],
[18, 2584],
[19, 4181],
[20, 6765],
[21, 10946],
[22, 17711],
[23, 28657],
[24, 46368],
[25, 75025],
[26, 121393],
[27, 196418],
[28, 317811],
[29, 514229],
[30, 832040],
[31, 1346269],
]
for i, _ in enumerate(sample):
if NumberTheory.fibonacci(sample[i][0]) != sample[i][1]:
return False
return True
def testSieveOfPrimes() -> bool:
sample = [
[0, 0],
[1, 0],
[180, 41],
[26, 9],
[350, 70],
[521, 98],
[307, 63],
[163, 38],
[181, 42],
[372, 73],
[421, 82],
[241, 53],
[229, 50],
[169, 39],
[442, 85],
[445, 86],
[338, 68],
[306, 62],
[56, 16],
[270, 57],
[499, 95],
[173, 40],
[18, 7],
[43, 14],
[218, 47],
[122, 30],
[265, 56],
[467, 91],
[381, 75],
[11, 5],
[409, 80],
[233, 51],
[1119, 187],
[6976, 896],
[4355, 594],
[7757, 984],
[3467, 486],
[5824, 764],
[7724, 980],
[1470, 232],
[7894, 997],
[6788, 873],
[7873, 994],
[6874, 885],
[3554, 497],
[4137, 569],
[7878, 995],
[3390, 477],
[2141, 323],
[4642, 626],
[2718, 396],
[7126, 912],
[1022, 172],
[5651, 743],
[4822, 649],
[2022, 306],
[6449, 837],
[2153, 325],
[1323, 216],
[6960, 893],
[2837, 412],
[4212, 576],
[2179, 327],
[1033, 174],
[33023, 3540],
[65798, 6572],
[39761, 4179],
[12379, 1478],
[25339, 2794],
[50093, 5143],
[98641, 9471],
[84959, 8272],
[90697, 8778],
[20898, 2350],
[63079, 6326],
[18369, 2104],
[23459, 2611],
[55337, 5620],
[55057, 5596],
[94463, 9111],
[22769, 2544],
[22501, 2516],
[68369, 6799],
[65315, 6524],
[72893, 7206],
[44969, 4672],
[69511, 6902],
[24371, 2705],
[32579, 3497],
[26017, 2862],
[84309, 8217],
[100043, 9595],
[86861, 8440],
[79355, 7776],
[14445, 1693],
[95418, 9197],
[1209025, 93544],
[526733, 43583],
[832339, 66339],
[350593, 30017],
[616581, 50358],
[787123, 62995],
[474923, 39612],
[320448, 27647],
[617049, 50394],
[232333, 20622],
[651727, 52944],
[524873, 43427],
[1008852, 79161],
[187573, 16970],
[432235, 36339],
[714479, 57629],
[669287, 54254],
[633133, 51574],
[964012, 75920],
[663127, 53800],
[1257461, 96995],
[172171, 15681],
[1112392, 86634],
[912533, 72211],
[409529, 34574],
[691575, 55914],
[742768, 59730],
[479430, 39964],
[108289, 10303],
[1228187, 94920],
[709431, 57257],
[1294061, 99610],
]
arr = None
for i, _ in enumerate(sample):
arr = NumberTheory.sieveOfPrimes(sample[i][0])
if len(arr) != sample[i][1]:
return False
for v in arr:
if not Primality.isPrime(v):
return False
return True