Sharedsupport / 2016-02-02-054844-dh.sagewsOpen in CoCalc
Examples for support purposes...

A Diffie-Hellman prime modulus... isn't prime.

See Hacker News: https://news.ycombinator.com/item?id=11014175

p_list = [0xCC, 0x17, 0xF2, 0xDC, 0x96, 0xDF, 0x59, 0xA4, 0x46, 0xC5, 0x3E, 0x0E, 0xB8, 0x26, 0x55, 0x0C, 0xE3, 0x88, 0xC1, 0xCE, 0xA7, 0xBC, 0xB3, 0xBF, 0x16, 0x94, 0xD8, 0xA9, 0x45, 0xA2, 0xCE, 0xA9, 0x5B, 0x22, 0x25, 0x5F, 0x92, 0x59, 0x94, 0x1C, 0x22, 0xBF, 0xCB, 0xC8, 0xC8, 0x57, 0xCB, 0xBF, 0xBC, 0x0E, 0xE8, 0x40, 0xF9, 0x87, 0x03, 0xBF, 0x60, 0x9B, 0x08, 0xC6, 0x8E, 0x99, 0xC6, 0x05, 0xFC, 0x00, 0xD6, 0x6D, 0x90, 0xA8, 0xF5, 0xF8, 0xD3, 0x8D, 0x43, 0xC8, 0x8F, 0x7A, 0xBD, 0xBB, 0x28, 0xAC, 0x04, 0x69, 0x4A, 0x0B, 0x86, 0x73, 0x37, 0xF0, 0x6D, 0x4F, 0x04, 0xF6, 0xF5, 0xAF, 0xBF, 0xAB, 0x8E, 0xCE, 0x75, 0x53, 0x4D, 0x7F, 0x7D, 0x17, 0x78, 0x0E, 0x12, 0x46, 0x4A, 0xAF, 0x95, 0x99, 0xEF, 0xBC, 0xA6, 0xC5, 0x41, 0x77, 0x43, 0x7A, 0xB9, 0xEC, 0x8E, 0x07, 0x3C, 0x6D]
p = 0
for num in p_list:
    p = (p << 8) + num
print "p =", p
p = 143319364394905942617148968085785991039146683740268996579566827015580969124702493833109074343879894586653465192222251909074832038151585448034731101690454685781999248641772509287801359980318348021809541131200479989220793925941518568143721972993251823166164933334796625008174851430377966394594186901123322297453
is_pseudoprime(p)
False
p.trial_division()
271
(p//271).trial_division(10^9)
13597
(p//271//13597).trial_division(10^8)
38894884397634366007356454548332370646972724268802781973440208895542936165564656473524541403310393405820598366261673173802130771236325314878371830363723788045821711985461441675679316058246609104355161134470046705337593170498462616195650378975298117141144096886684800236261920005248055422089305813639519
%time (p//271//13597).is_prime()
False CPU time: 0.00 s, Wall time: 0.04 s
(p//271//13597).is_pseudoprime()
False
len((p//271//13597).bits())
1002
%timeit is_prime(p)
625 loops, best of 3: 843 µs per loop
q = next_prime(2^1024)
%time q.is_pseudoprime()
%time q.is_prime()
True CPU time: 0.00 s, Wall time: 0.00 s True CPU time: 4.14 s, Wall time: 4.13 s
q = next_prime(2^2048)
%time q.is_pseudoprime()
%time q.is_prime()
True CPU time: 0.00 s, Wall time: 0.02 s True CPU time: 66.12 s, Wall time: 66.13 s