NOTE ON A MERSENNE NUMBER

BY R. E. POWERS

I have recently determined by the computation of Lucas' series 4, 14, 194, ...[1] that the number N = 2^241 - 1 is composite, since the 240th term of the series is congruent to

- 98 6778335538 8807227981 3604528486 9326522489 7467133466 0099172867 1619979800 (mod N).

This term would be zero if N were prime.
The square of each term was obtained by means of a computing machine, D. N. Lehmer's cross-multiplication[2] being used; and these squares, diminished by 2, were divided by N by hand, with the aid of a table of the 1000 multiples of N: N, 2N, 3N, ..., 1000N, the quotients being thus obtained three or more digits at a time, and the computation was checked throughout by the four moduli 9, 10^3+1, 10^4+1, and 10^7+1.

DENVER COLORADO

[1] This Bulletin, vol. 38 (1932), p.383.
[2] American Mathematical Monthly, vol. 30 (1923), p. 67, and vol 33 (1926), p.199.

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