I dont think that testing whether huge numbers are prime or not is quite as easy as you assume.

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

It's pretty easy. There are ways to test primarily such that constructing a counterexample would be an important mathematical result.

https://en.wikipedia.org/wiki/Baillie–PSW_primality_test

> The power of the Baillie-PSW test comes from the fact that these lists of strong Fermat pseudoprimes and strong Lucas pseudoprimes have no known overlap. There is even evidence that the numbers in these lists tend to be different kinds of numbers.

It might be "easy" but is it quick enough to be tolerated as part of a build?

A primality certificate could be included that allows the prime to be verified quickly during the build. This certificate for the 2048-bit prime took 90 seconds to generate, and can be verified in 3 seconds.

http://web.mit.edu/andersk/Public/socat-prime.pl

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

The primality test of the original number using gp that archgoon posted takes 6ms on my Sandy Bridge laptop, that's plenty fast. (The new number takes a minute to check, though, so that might really be too long)

Maxima's primep takes 360ms on the 1024-bit one for me, so seems quick enough to stick into the build.

It sounds like the chance if it passing the test is around 10^-15 using the default values; which seems sufficient for a build test which is run many times.

If this the alternative, it very well might be.

Just build your sensitive hard coded primes in a separate object file. It rarely needs updating.