Ralph Ernest Powers

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

Life

Details of his life are little-known, though he appears to have been an employee of the Denver and Rio Grande Western Railroad. However, Powers was apparently the first mathematician to demonstrate that the Mersenne number M₁₀₇ = 2¹⁰⁷ − 1 was indeed prime. This was published in his article Certain composite Mersenne's numbers in 1916. Sometimes, mathematical textbooks attribute this result to one E. Fauquembergue, but it appears that many of Fauquembergue's claims were later demonstrated as erroneous; thus, many prefer recognizing Powers as the discoverer, including the well-known Internet resource The Prime Pages.

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