(phdSrSSKrSSKrSS/rS\S\S\4SjrS \S\4S jrS \S \S\4S jr S \S\4Sjr S\S\4Sjr S\S\S\4Sjr \ S:Xa`\"S5 SSKr\"S5H?r\R$"5urr\(a O#\S-S:XdM+\(dM4\"S\-5 MA \"S5 gg)zNumerical functions related to primes. Implementation based on the book Algorithm Design by Michael T. Goodrich and Roberto Tamassia, 2002. Ngetprimeare_relatively_primepqreturnc,US:wa XU-pUS:waM U$)zDReturns the greatest common divisor of p and q >>> gcd(48, 180) 12 r)rrs >> is_prime(2) True >>> is_prime(42) False >>> is_prime(41) True r>rrrrF)rr&)r rs r is_primer)vs?{%% QJ %V,A *&a% 88r nbitsczUS:de[RRU5n[U5(aU$M3)zReturns a prime number that can be stored in 'nbits' bits. >>> p = getprime(128) >>> is_prime(p-1) False >>> is_prime(p) True >>> is_prime(p+1) False >>> from rsa import common >>> common.bit_size(p) == 128 True r)rrread_random_odd_intr))r*integers r rrs> 199 ++11%8 G  N r r$bc"[X5nUS:H$)zReturns True if a and b are relatively prime, and False if they are not. >>> are_relatively_prime(2, 3) True >>> are_relatively_prime(2, 4) False r)r )r$r.r!s r rrs A A 6Mr __main__z'Running doctests 1000x or until failureidz%i timesz Doctests done)__doc__ rsa.commonr rsa.randnum__all__intr rboolr&r)rr__name__printdoctestrcounttestmodfailurestestsr r r r?s   - .  3  3  3  42c2c2d2j9S9T94CC8 C C D  z 34t#OO-5   3;!  *u$ %  /r