galois.random_prime

galois.random_prime(bits: int) → int

Returns a random prime $p$ with $b$ bits, such that $2^{b} \leq p < 2^{b + 1}$ .

This function randomly generates integers with $b$ bits and uses the primality tests in is_prime() to determine if $p$ is prime.

Parameters¶

bits: int¶: The number of bits in the prime $p$ .

Returns¶

A random prime in $2^{b} \leq p < 2^{b + 1}$ .

See also

prev_prime, next_prime

References¶

https://en.wikipedia.org/wiki/Prime_number_theorem

Examples¶

Generate a random 1024-bit prime.

In [1]: p = galois.random_prime(1024); p
Out[1]: 342888254381288058719884227089257890035191369754956728808545621653174405204152196726108062195877222681572514358920019512197766156755922078457126522106775392471669510236938863244957186851350124705009053894994299675418748642749923249258049993689588937572422085001929013887596860995187013957668641055951613002757

In [2]: galois.is_prime(p)
Out[2]: True

$ openssl prime 236861787926957382206996886087214592029752524078026392358936844479667423570833116126506927878773110287700754280996224768092589904231910149528080012692722763539766058401127758399272786475279348968866620857161889678512852050561604969208679095086283103827661300743342847921567132587459205365243815835763830067933
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is prime