Using results from
J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime
bases, Math. Comp. 86(304):985-1003, 2017.
teach primes(6) to enumerate primes up to 2^64 - 1. Until Sorenson
and Webster's paper, we did not know how many strong speudoprime tests
were required when testing alleged primes between 3825123056546413051
and 2^64 - 1.
Adapted from: FreeBSD
false positives for products of primes larger than 2^16. For example,
before this commit:
$ /usr/games/primes 4295360521 4295360522
4295360521
but
$ /usr/games/factor 4295360521
4295360521: 65539 65539
or
$ /usr/games/primes 3825123056546413049 3825123056546413050
3825123056546413049
yet
$ /usr/games/factor 3825123056546413049
3825123056546413049: 165479 23115459100831
or
$ /usr/games/primes 18446744073709551577
18446744073709551577
although
$ /usr/games/factor 18446744073709551577
18446744073709551577: 139646831 132095686967
Incidentally, the above examples show the smallest and largest cases that
were erroneously stated as prime in the range 2^32 .. 3825123056546413049
.. 2^64; the primes(6) program now stops at 3825123056546413050 as
primality tests on larger integers would be by brute force factorization.
In addition, special to the NetBSD version:
. for -d option, skip first difference when start is >65537 as it is incorrect
. corrected usage to mention both the existing -d as well as the new -h option
For original FreeBSD commit message by Colin Percival, see:
http://svnweb.freebsd.org/base?view=revision&revision=272166
christos