A positive integer 
is a veryprime iff all primes 
satisfy
![{|2[n (mod p)]-p|<=1 very strong; |2[n (mod p)]-p|<=sqrt(p) strong; |2[n (mod p)]-p|<=p/2 weak.](/images/equations/Veryprime/NumberedEquation1.svg) |
(1)
|
The weak veryprimes are then 2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 43, 47, 53, 67, 73, 103, 107, 137, 157, 173, 227, 347, 487, 773, ... (OEIS A050264),
the strong veryprimes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 37, 43, 47, 53, 67, 73,
137, 227, ..., and the very strong veryprimes are 2, 3, 5, 7, 11, 13, 17, 19, 23,
37, 43, 47, 53, 67, 73, 137, ..., with no others in the first 
primes.
