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Payam Number


Given an integer e>=2, the Payam number E_+/-(e) is the smallest positive odd integer k such that for every positive integer n, the number k·2^n+/-1 is not divisible by any primes p such that the multiplicative order of 2  (mod p) is less than or equal to e. Payam numbers are good candidates for searching for Proth primes, i.e., primes of the form k·2^n+1, as well as primes of the form k·2^n-1.

The first few values of E_+(n) for n=2, 3, ... are 3, 9, 15, 105, 105, 105, 105, 105, 165, 165, 75075, ... (OEIS A083556), and the first few values of E_-(n) are 3, 3, 45, 45, 45, 45, 45, 45, 45, 2145, ... (OEIS A083391).


See also

Proth Prime

This entry contributed by David Terr

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References

Sloane, N. J. A. Sequences A083391 and A083556 in "The On-Line Encyclopedia of Integer Sequences."Smith, R. "A Co-Ordinated Search for Primes in the Payam Number Series." http://home.btclick.com/rwsmith/pp/payam3.htm.

Referenced on Wolfram|Alpha

Payam Number

Cite this as:

Terr, David. "Payam Number." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/PayamNumber.html

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