Mersenne Numbers & Mersenne Primes Bibliography

[blue dot] Origin of this bibliography
This list evolved from a Table of Contents that I compiled in the 1980's as I visited various libraries (especially Stanford) and photocopied whatever I could on Mersenne Numbers. I have a few more articles to include, and I have a lot of references, but without any hard or soft copy, which I may also list here.
[blue dot] Thanks et Merci
Entries 65 and 66 (Ferrier) and 67 (Lucas) were put into HTML by Edward Brisse.
Entry 68 was translated into English by Edward Brisse and Joseph E. Houle.
Entries 3, 7, 8, 9, 10, 11, 16, 18, 20, 21, 22, 27, 28, 39, 40, and 48 were put into HTML by Conrad Curry.
[blue dot] Different formats
Blue Buttons link to the article in plain text
Red Buttons link to the article in HTML (without subscript support)
Yellow Buttons link to the article in HTML (with subscript support)
         This should read as n squared: n2
         This should read as m to the power of n squared: mn2
[blue dot] Sequence
Entries are ordered by publication date.
69
link to HTML (with subscripts) version of paper #69
M. Mersenne Cogitata Physico-Mathematica, Preface, Chapter XIX, 1644. Translated from the Latin, as quoted by E. Lucas, by S. Kravitz, translation edited by D. Lind. Published in the Fibonacci Quarterly, 1969. Notes. Authorization.
67
link to HTML (with subscripts) version of paper #67
É. Lucas Récréations Mathématiques,
Paris Gauthier-Villars (1883), tome II, Note II, Sur les nombres de Fermat et de Mersenne, p.230-235
See [68] in English.
68
link to HTML (with subscripts) version of paper #68
É. Lucas Mathematical Recreations,
Paris Gauthier-Villars (1883), v. II, Note II, On Fermat and Mersenne Numbers, p.230-235
Voir [67] en Français.
2
link to text version of paper #2
R. E. Powers The Tenth Perfect Number
Amer. Math. Monthly
v. XVIII, no. 11, Nov. 1911, p. 195-197
M89 is prime. First proof that Mersenne was wrong
3
link to text version of paper #3
link to HTML (with subscripts) version of paper #3
R. E. Powers On Mersenne's Numbers
P. London Math. Soc.
Record of preceedings at meetings
s. 2, v. 13, 1914, p. xxxix
M107 is prime
4 A. E. Western On Lucas's and Pepin's Tests for the Primeness of Mersenne Numbers
J. London Math. Soc.
v. 7, 1932, p. 130-137
Uses term Computers. Doesn't mention M229
5 D. H. Lehmer Note on Mersenne Numbers
BAMS
v. 38, 1932, p. 383-4
70 hours to find M149 composite. M257 is composite
6
link to HTML version of paper #6
link to text version of paper #6
R. E. Powers Note on a Mersenne Number
BAMS
v. 40, 1934, p. 883
M241 is composite
7
link to HTML (with subscripts) version of paper #7
D. H. Lehmer On Lucas's Test for the Primality of Mersenne's Numbers
J. London Math. Soc.
v. 10, 1935, p. 162-165
Wanted List: M157, M167, M193, M199, M227, and M229
8
link to HTML (with subscripts) version of paper #8
R. C. Archibald Mersenne's Numbers
Scripta Mathematica
v. 3, 1935, p. 112-119
A great history. Mersenne predicted M131071
9
link to HTML (with subscripts) version of paper #9
link to text version of paper #9
H. S. Uhler Notes
#23 A New Result Concerning a Mersenne Number
MTAC
v. 1, 1944, p. 333
M157 is Composite
10
link to HTML (with subscripts) version of paper #10
link to text version of paper #10
H. S. Uhler Notes
#33 A New Result Concerning a Mersenne Number
MTAC
v. 1, 1944, p. 404
M167 is Composite
11
link to HTML (with subscripts) version of paper #11
H. S. Uhler Queries--Replies
#55 A New Result Concerning a Mersenne Number
MTAC
v. 2, 1945, p. 94
M229 is Composite
12 C. B. Barker Proof that the Mersenne Number M167 is Composite
BAMS
v. 51, 1945, p. 389
Uhler found it first [10,13] and Barker's residue is wrong [19]
13 H. S. Uhler Note on the Mersenne Numbers M157 and M167
BAMS
v. 52, 1945?1946?, p. 178, MR7p273
His & Barker's M167 [10,12]
65
link to HTML (with subscripts) version of paper #65
J. Ferrier Les nombres premiers,
Paris Vuibert (1947), Chapitre IX, Les nombres de Mersenne, p.40-41
See [66] in English.
66
link to HTML (with subscripts) version of paper #66
J. Ferrier Prime Numbers,
Paris Vuibert (1947), Chapter IX, Mersenne Primes, p.40-41
Voir [65] en Français.
14 H. S. Uhler On Mersenne's Number M199 and Lucas's Sequences
BAMS
v. 53, 1947, p. 163-164, MR7p413
M199 is composite. Starts on M227
15 D. H. Lehmer On the Factors of 2n+-1
BAMS
v. 53, 1947, p. 164-167
Easy factors for poor Uhler's M167 & M229
16
link to HTML (with subscripts) version of paper #16
R. C. Archibald
(Editor & Reviewer)
Note 434[F]
MTAC
v. 2, 1947, p. 341
review of [15]
1 Ø. Ore Number Theory and Its History
1948, p. 72
Portrait of Mersenne (29kb GIF)
17 H. S. Uhler On Mersenne's Number M227 and Cognate Data
BAMS,
v. 54, no. 4 (April 1948) p. 378-380
M227 is composite. Starts on M193, the last one
18
link to HTML (with subscripts) version of paper #18
R. C. Archibald
(Editor & Reviewer)
Mersenne Numbers
Note 98
MTAC
v. 3, 1949, p. 398
On all 55 original Mersenne Numbers. Uhler found M193 composite
62
link to text version of paper #62
link to HTML version of paper #62
link to HTML (with subscripts) version of paper #62
J. C. P. Miller
D. J. Wheeler
Large Prime Numbers
Nature
v. 168, (1951), p. 838
The dawn of the computer age. Edsac computer breaks Lucas's record. Details in [63].
63
link to text version of paper #63
J. C. P. Miller Large Primes
Eureka
no. 14, (1951), p. 10, 11
How the Edsac set the record announced in [62].
64 H. S. Uhler Many-Figure Values of the Logarithms of the Year of Destiny and Other Constants
Scripta Mathematica
v. 17, nos 3-4 (Sept.-Dec. 1951), p. 202-208
Error checking of manual computations of large numbers.
19
link to text version of paper #19
link to HTML version of paper #19
H. S. Uhler A Brief History of the Investigations on Mersenne's Numbers and the Latest Immense Primes
Scripta Mathematica
v. 18, 1952, p. 122-131
Humorous History. Barker's "fiasco"
20
link to HTML (with subscripts) version of paper #20
D. H. Lehmer
(Editor & Reviewer)
Recent Discoveries of Large Primes
Note 131
MTAC
v. 6, 1952, p. 61
Announces Discovery of 13th & 14th Mersenne Primes, M521 & M607
21
link to HTML (with subscripts) version of paper #21
link to text version of paper #21
D. H. Lehmer
(Editor & Reviewer)
A New Mersenne Prime
Note 138
MTAC
v. 6, 1952, p. 205
Announces Discovery of 15th Mersenne Prime, M1279. 13 minutes 25 secconds
22
link to HTML (with subscripts) version of paper #22
link to text version of paper #22
D. H. Lehmer
(Editor & Reviewer)
Two New Mersenne Primes
Note 146
MTAC
v. 7, 1953, p. 72
Announces Discovery of 16th & 17th Mersenne Primes, M2203 & M2281
23 H. S. Uhler On the 16th and 17th Perfect Numbers
Scripta Mathematica
v. 19, 1953, p. 128-131
M2203: 59 minutes. M2281: 66 minutes.
24
link to HTML (with subscripts) version of paper #24
link to HTML version of paper #24
link to text version of paper #24
R. M. Robinson Mersenne and Fermat Numbers
PAMS
v. 5, 1954, p. 842-846
Discovering the 13th through 17th Mersenne Primes. Residues at UCLA. Turing searched.
25 I. J. Good Conjectures Concerning the Mersenne Numbers
MTAC
v. 9, 1955, p 120-121
Good was a cyrptographer in UK during WWII
26 R. M. Robinson Some Factorizations of Numbers of the Form 2n+-1
MTAC
v. 11, 1957, p. 265-268
Finds f1 for M109 & M157
27
link to HTML (with subscripts) version of paper #27
H. Riesel Mersenne Numbers
MTAC
v. 12, 1958, p. 207-213
Discovery of 18th Mersenne Prime: M3217. 5h 30m. Some factors in error: see [28]
28
link to HTML (with subscripts) version of paper #28
J. L. Selfridge MTE 271
MTAC
v. 13, 1959, p. 142
Some corrections to [27]
29 J. Brillhart & G. D. Johnson On the Factors of Certain Mersenne Numbers
Math. Comp.
v. 14, 1960, p. 365-369
Some factors
30 A. Hurwitz & J.L. Selfridge Fermat numbers and perfect numbers
NAMS
v. 8, 1961, p. 601, abstract 587-104
Announces 19th & 20th Mersenne Primes: M4253 & M4423
31 E. Karst New Factors of Mersenne Numbers
Math. Comp.
v. 15, 1961, p. 51
Some factors
32 S. Kravitz Divisors of Mersenne Numbers 10,000 < p < 15,000
Math. Comp.
v. 15, 1961, p. 292-293
IBM 650. On the distribution of k's.
33 E. Karst Some New Divisors of Mersenne Numbers
BIT
v. 2, 1962, p. 90
Some Factors, some absurd
34 E. Karst Search Limits on Divisors of Mersenne Numbers
BIT
v. 2, 1962, p. 224-227
Some Factors
35
link to HTML (with subscripts) version of paper #35
link to HTML version of paper #35
link to text version of paper #35
A. Hurwitz New Mersenne Primes
Math. Comp.
v. 16, 1962, p. 249-251
Discovery of 19th & 20th MP. Residues 3300 < p < 5000, 8191. Some errors [42].
36 H. Riesel All Factors q < 10**8 in All Mersenne Numbers 2p-1, p Prime < 10**4
Math. Comp.
v. 16, 1962, p. 478-482
Some errors, see [37]
37 J. D. Brillhart MTE 340
MTAC
v. 17, 1963, p. 486
Corrections to [36]
38 J. D. Brillhart On the Factors of Certain Mersenne Numbers II
Math. Comp.
v. 18, 1964, p. 87-92, MR 28 #2992
Corrections to [36]
39 link to HTML (with subscripts) version of paper #39 J. L. Selfridge & A. Hurwitz Fermat Numbers and Mersenne Numbers
Math. Comp.
v. 18, 1964, p. 146-148
Residues 5000 < p < 6000
40 link to HTML (with subscripts) version of paper #40 S. Kravitz & M. Berg Lucas's Test for Mersenne Numbers, 6000 < p < 7000
Math. Comp.
v. 18, 1964, p. 148-9, MR28#1152
Residues. IBM 7090, about 3 hours per test.
41 H. Riesel Note on the Congruence ap-1 = 1 (mod p2)
Math. Comp.
v. 18, 1964, p. 149
 
42 D. B. Gillies Three New Mersenne Primes and a Statistical Theory
Math. Comp.
v. 18, 1964, p. 93-97
Discovery of 21st through 23rd MP, M9689, M9941, & M11213. Residues & Factors. Corrections to [35]. Some errors [51].
43 D. Shanks (Reviewer) S. Kravitz & J. S. Madachy
Divisors of Mersenne Numbers, 20,000 < p < 100,000
Review #113, Math. Comp.
v. 19, 1965, p. 686
Debunks Karst
44 A. Rotkiewicz Sur les Nombres de Mersenne Dépourvus de Diviseurs Carrés et Sur les Nombres Naturels n, Tels n**2|2**n-2
Matematicky Vesnik
2, v. 17, 1965, p. 78-80
 
45 S. Kravitz Distributions of Mersenne Divisors
Math. Comp.
v. 20, 1966, p. 448-449
More on the distribution of k's
46 J. R. Ehrman Prime Divisors of Mersenne Numbers
TN-66-40, Sept. 1966, SLAC, Stanford, Calif.
 
47 J. R. Ehrman The Number of Prime Divisors of Certain Mersenne Numbers
Math. Comp.
v. 21, 1967, p. 700-704
 
48 link to HTML (with subscripts) version of paper #48 D. Shanks & S. Kravitz On the Distribution of Mersenne Divisors
Math. Comp.
v. 21, 1967, p. 97-101
 
49 B. Tuckerman The 24th Mersenne Prime
PNAS
v. 68, 1971, p. 2319-2320
Discovery of M19937. 35 minutes
50 J. Brillhart, D. H. Lehmer & J. L. Selfridge New Primality Criteria and Factorizations of 2n+-1
Math. Comp.
v. 29, 1975, p. 620-647
Photo of Lehmer. Still no factors for M199 M227 M257
51 B. Tuckerman Math. Comp.
v. 31, 1977, p. 1051, MR56#233
Correction to [42]
52 D. Slowinski Searching for the 27th Mersenne Prime
J. Rec. Math.
v. 11(4), 1978-79, p. 258-261, MR 80g #10013
Discovery of M44497. Typesetting error of M19737 for M19937.
53 P. Ribenboim 13 Lectures on Fermat's Last Theorem
Springer Verlag, 1979, pp. 20, 24, 27, 154
MP squarefree for all q < 9710
54 C. Noll & L. Nickel The 25th and 26th Mersenne Primes
Math. Comp.
v. 35, 1980, p. 1387-1390
M21701: 7 hours 40 minutes 20 seconds. M23209.
55 C. L. Noll Discovering the 26th Mersenne Prime
Dr. Dobb's Journal
v. 4, issue 6, no. 36, June/July 1979, p. 4-5
M23209.
56 L. A. Nickel & C. L. Noll The 25th Mersenne Prime
Dr. Dobb's Journal
v. 4, issue 6, no. 36, June/July 1979, p. 6
M21701
57 S. S. Wagstaff, Jr. Divisors of Mersenne Numbers
Math. Comp.
v. 38, 1983, p. 385-397
 
58 G. McC. Haworth Primality-testing Mersenne Numbers
AAMS
v. 4, no. 2, 1983, p. 196, 83T-10-82
 
59 R. P. Brent New factors of Mersenne numbers, III
AAMS
v. 4, no. 2, 1983, p. 197, 83T-10-138
Factors M227
60 G. McC. Haworth Primality-testing Mersenne Numbers, II
AAMS
v. 7, no. 2, 1986, p. 224-5, 86T-11-57
 
61 I. Peterson Priming for a Lucky Strike
Science News
v. 133, no. 6, 1988, p. 85
Missing M110503 found

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http://primes.utm.edu/mersenne/LukeMirror/biblio.htm -- Revised: 9 April 1997
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