# 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 ShanthaPrime 2013-03-22 17:49:54 2013-03-22 17:49:54 PrimeFan (13766) PrimeFan (13766) 26 PrimeFan (13766) Definition msc 11A41