But the biggest reason that the largest known primes have this form is that they are subject to a much faster special-form primality test. https://en.wikipedia

But the biggest reason that the largest known primes have this form is that they are subject to a much faster special-form primality test. https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality_test https://en.wikipedia.org/wiki/Lucas%E2%80%93Lehmer_primality... There's no known general-form primality test that is nearly as fast for numbers of corresponding sizes.