Thread: Distribution of primegaps View Single Post
2018-07-29, 15:23   #34
Dr Sardonicus

Feb 2017
Nowhere

3×1,999 Posts

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

$\varphi(n)=2$.

(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.

Last fiddled with by Dr Sardonicus on 2018-07-29 at 15:48