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Veryprime


A positive integer n is a veryprime iff all primes p<=sqrt(n) 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.
(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 100000 primes.


See also

Quiteprime

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References

Ferry, J. "RE: Veryprimes defined." sci.math posting, 09 Sep 1999.Sloane, N. J. A. Sequence A050264 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Veryprime

Cite this as:

Weisstein, Eric W. "Veryprime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Veryprime.html

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