galois.random_prime¶

galois.random_prime(bits)¶

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

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

Parameters¶

bits : int¶

The number of bits in the prime \(p\).

Returns¶

A random prime in \(2^b \le p < 2^{b+1}\).

Return type¶

int

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]: 337170697340901321530689124365059949940956659342656976423844495973329386241888037569679644531047631616478085335901195156195069469595051900822947340783559615283038160062304193402408963425290338469529165694911556644387057509755704936195470051961695566712948400744620864881520315746529798972435197520698754024171

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

$ openssl prime 236861787926957382206996886087214592029752524078026392358936844479667423570833116126506927878773110287700754280996224768092589904231910149528080012692722763539766058401127758399272786475279348968866620857161889678512852050561604969208679095086283103827661300743342847921567132587459205365243815835763830067933
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is prime