Quote:
Originally Posted by Bobby Jacobs
We should try primes mod n for different values of n.

OK, I tried a couple  the n's with
.
(BTW, I disregard the prime factors of n.)
For n = 4, the first odd prime is p = 3, so the residue class 3 mod 4 takes an early lead. It keeps it for some time:
Code:
? v=vector(2);forprime(p=3,100000,r=p%4;if(r==1,v[1]++,v[2]++);if(v[1]>v[2],print(p" "v);break))
26861 [1473, 1472]
For n = 6, the first prime not dividing 6 is 5, so the residue class 5 mod 6 takes an early lead. I checked up to 2^31, and up to that limit, 1 (mod 6) had yet to depose it.
EDIT: According to
Prime Races [which I recommend reading], 1 mod 6 doesn't take the lead until
p = 608,981,813,029.