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# Shantha prime

A Shantha prime $p$ is a prime number of the form $p=3^{q}-2$ with $q$ being a Mangammal prime. 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.

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## Mathematics Subject Classification

11A41*no label found*

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