Ralph Ernest Powers Explained

Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers.

He is credited with discovering the Mersenne primes and, in 1911 and 1914 respectively.^{[1] [2]} In 1934 he verified that the Mersenne number is composite.^[3]

Life

Powers was born in Fountain, Colorado Territory. Details of his life are little-known,^[4] though he appears to have been an employee of the Denver and Rio Grande Western Railroad.^[5]

Soon after Powers announced the discovery of, the Frenchman E. Fauquembergue claimed that he had discovered it earlier, but many of Fauquembergue's other claims were later demonstrated as erroneous; thus, many prefer recognizing Powers as the discoverer, including the well-known Internet resource the PrimePages.

After his own discoveries of Mersenne primes in 1911 and 1914, no Mersenne primes were discovered until Raphael M. Robinson used a computer to find the next two, on January 30, 1952, the night before Powers's death.

Works

• ‘The Tenth Perfect Number', American Mathematical Monthly, Vol. 18 (1911), pp. 195–7
• ’On Mersenne's Numbers', Proceedings of the London Mathematical Society, Vol. 13 (1914), p. xxxix
• 'A Mersenne Prime', Bulletin of the American Mathematical Society, Vol. 20, No. 10 (1914), p. 531
• ’Certain composite Mersenne's numbers', Proceedings of the London Mathematical Society Vol. 15 (1916), p. xxii
• (with D. H. Lehmer) 'On Factoring Large Numbers', Bulletin of the American Mathematical Society, Vol. 37. No. 10 (1931), pp. 770–76
• ’Note on a Mersenne Number', Bulletin of the American Mathematical Society, Vol. 40, No. 12 (1934), p. 883

See also

• Continued fraction factorization

External links

• The Prime Pages website
• Mersenne and Fermat Numbers (Robinson); brief treatment of Powers
• The Tenth Perfect Number, an article by Powers announcing the primality of M₈₉

Notes and References

1. American Mathematical Monthly . The Tenth Perfect Number . R. E. Powers . 18 . 11 . 195–197 . 1911 . 2972574 . The article is signed "DENVER, COLORADO, June, 1911" . 10.2307/2972574.
2. http://plms.oxfordjournals.org/content/s2-13/1/1.1.full.pdf
3. Bulletin of the American Mathematical Society . Note on a Mersenne Number . R. E. Powers . 40 . 12 . 1934 . 883 . 10.1090/s0002-9904-1934-05994-9. free .
4. https://www.ams.org/journals/mcom/1952-06-038/S0025-5718-52-99396-4/S0025-5718-52-99396-4.pdf Obituary
5. Book: Hugh C. Williams. Édouard Lucas and Primality Testing. 1998. Wiley. 978-0-471-14852-4.