Shantha prime

A Shantha prime $p$ is a prime number of the form $p=3^{q}-2$ with $q$ being a Mangammal prime (http://planetmath.org/MangammalPrime). The smallest Shantha prime is $7=3^{2}-2$ . The next is $3^{541}-2$ and has 259 digits. Shantha primes are very rare among the smaller numbers. The above formulation generates mostly composite numbers.

References

1 A. K. Devaraj, ”Euler’s Generalization of Fermat’s Theorem-A Further Generalization”, in Proceedings of Hawaii International Conference on Statistics, Mathematics & Related Fields, 2004.

Title	Shantha prime
Canonical name	ShanthaPrime
Date of creation	2013-03-22 17:49:54
Last modified on	2013-03-22 17:49:54
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	26
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A41