Primality proof for n = 5928943045730601679673230900230929495199307291013218575943:

Take b = 2.

b^(n-1) mod n = 1.

21691107791071112804746088983950791 is prime.
b^((n-1)/21691107791071112804746088983950791)-1 mod n = 3018516012836291684176828116465051729467219630066324330537, which is a unit, inverse 4346460420019705969402116216903654131093495673705140504017.

(21691107791071112804746088983950791) divides n-1.

(21691107791071112804746088983950791)^2 > n.

n is prime by Pocklington's theorem.