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 |
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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 |