A new Mersenne prime

Colquitt, W. N.; Welsh, L.

doi:10.1090/S0025-5718-1991-1068823-9

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A new Mersenne prime

Authors: W. N. Colquitt and L. Welsh
Journal: Math. Comp. 56 (1991), 867-870
MSC: Primary 11A41; Secondary 11Y11
MathSciNet review: 1068823
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Abstract: The number ${2^{110503}} - 1$ is a Mersenne prime. There are exactly two Mersenne exponents between 100000 and 139268, and there are no Mersenne exponents between 216092 and 353620. Thus, the number ${2^{132049}} - 1$ has been verified as the 30th Mersenne prime in order of size.

[1] D. H. Bailey, personal communication.
[2] G. Haworth, personal communication (graciously supplied both information and verification data for ).
[3] Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms; Addison-Wesley Series in Computer Science and Information Processing. MR 633878 (83i:68003)
[4] Sidney Kravitz and Murray Berg, Lucas’ test for Mersenne numbers, 6000<𝑝<7000, Math. Comp. 18 (1964), 148–149. MR 0157924 (28 #1152), http://dx.doi.org/10.1090/S0025-5718-1964-0157924-9
[5] D. H. Lehmer, On Lucas's test for the primality of Mersenne's numbers, J. London Math. Soc. 10 (1935), 162-165.
[6] S. McGrogan, personal communication.
[7] H. Nelson, personal communication.
[8] Curt Noll and Laura Nickel, The 25th and 26th Mersenne primes, Math. Comp. 35 (1980), no. 152, 1387–1390. MR 583517 (81k:10010), http://dx.doi.org/10.1090/S0025-5718-1980-0583517-4
[9] William H. Press, Brian P. Flannery, Saul A. Teukolsky, and William T. Vetterling, Numerical recipes, Cambridge University Press, Cambridge, 1986. The art of scientific computing. MR 833288 (87m:65001a)
[10] David Slowinski, Searching for the 27th Mersenne prime, J. Recreational Math. 11 (1978/79), no. 4, 258–267. MR 536930 (80g:10013)
[11] -, personal communication.
[12] J. Young, personal communication.

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