Mersenne Numbers & Mersenne Primes Bibliography 
69

M. Mersenne  Cogitata PhysicoMathematica, 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

É. Lucas  Récréations Mathématiques,
Paris GauthierVillars (1883), tome II, Note II, Sur les nombres de Fermat et de Mersenne, p.230235 
See [68] in English. 
68

É. Lucas  Mathematical Recreations,
Paris GauthierVillars (1883), v. II, Note II, On Fermat and Mersenne Numbers, p.230235 
Voir [67] en Français. 
2

R. E. Powers  The Tenth Perfect Number
Amer. Math. Monthly v. XVIII, no. 11, Nov. 1911, p. 195197 
M89 is prime. First proof that Mersenne was wrong 
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. 130137 
Uses term Computers. Doesn't mention M229 
5  D. H. Lehmer  Note on Mersenne Numbers
BAMS v. 38, 1932, p. 3834 
70 hours to find M149 composite. M257 is composite 
6

R. E. Powers  Note on a Mersenne Number
BAMS v. 40, 1934, p. 883 
M241 is composite 
7

D. H. Lehmer  On Lucas's Test for the Primality of Mersenne's Numbers
J. London Math. Soc. v. 10, 1935, p. 162165 
Wanted List: M157, M167, M193, M199, M227, and M229 
8

R. C. Archibald  Mersenne's Numbers
Scripta Mathematica v. 3, 1935, p. 112119 
A great history. Mersenne predicted M131071 
9

H. S. Uhler  Notes
#23 A New Result Concerning a Mersenne Number MTAC v. 1, 1944, p. 333 
M157 is Composite 
10

H. S. Uhler  Notes
#33 A New Result Concerning a Mersenne Number MTAC v. 1, 1944, p. 404 
M167 is Composite 
11

H. S. Uhler  QueriesReplies
#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

J. Ferrier  Les nombres premiers,
Paris Vuibert (1947), Chapitre IX, Les nombres de Mersenne, p.4041 
See [66] in English. 
66

J. Ferrier  Prime Numbers,
Paris Vuibert (1947), Chapter IX, Mersenne Primes, p.4041 
Voir [65] en Français. 
14  H. S. Uhler  On Mersenne's Number M199 and Lucas's Sequences
BAMS v. 53, 1947, p. 163164, MR7p413 
M199 is composite. Starts on M227 
15  D. H. Lehmer  On the Factors of 2n+1
BAMS v. 53, 1947, p. 164167 
Easy factors for poor Uhler's M167 & M229 
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. 378380 
M227 is composite. Starts on M193, the last one 
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

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

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  ManyFigure Values of the Logarithms of the Year of Destiny
and Other Constants
Scripta Mathematica v. 17, nos 34 (Sept.Dec. 1951), p. 202208 
Error checking of manual computations of large numbers. 
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. 122131 
Humorous History. Barker's "fiasco" 
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

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

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. 128131 
M2203: 59 minutes. M2281: 66 minutes. 
24

R. M. Robinson 
Mersenne and Fermat Numbers
PAMS v. 5, 1954, p. 842846 
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 120121 
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. 265268 
Finds f1 for M109 & M157 
27

H. Riesel  Mersenne Numbers
MTAC v. 12, 1958, p. 207213 
Discovery of 18th Mersenne Prime: M3217. 5h 30m. Some factors in error: see [28] 
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. 365369 
Some factors 
30  A. Hurwitz & J.L. Selfridge  Fermat numbers and perfect numbers
NAMS v. 8, 1961, p. 601, abstract 587104 
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. 292293 
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. 224227 
Some Factors 
35

A. Hurwitz  New Mersenne Primes
Math. Comp. v. 16, 1962, p. 249251 
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 2p1, p Prime < 10**4
Math. Comp. v. 16, 1962, p. 478482 
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. 8792, MR 28 #2992 
Corrections to [36] 
39  J. L. Selfridge & A. Hurwitz  Fermat Numbers and Mersenne Numbers
Math. Comp. v. 18, 1964, p. 146148 
Residues 5000 < p < 6000 
40  S. Kravitz & M. Berg  Lucas's Test for Mersenne Numbers, 6000 < p < 7000
Math. Comp. v. 18, 1964, p. 1489, MR28#1152 
Residues. IBM 7090, about 3 hours per test. 
41  H. Riesel  Note on the Congruence ap1 = 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. 9397 
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**22**n2
Matematicky Vesnik 2, v. 17, 1965, p. 7880 

45  S. Kravitz  Distributions of Mersenne Divisors
Math. Comp. v. 20, 1966, p. 448449 
More on the distribution of k's 
46  J. R. Ehrman  Prime Divisors of Mersenne Numbers
TN6640, Sept. 1966, SLAC, Stanford, Calif. 

47  J. R. Ehrman  The Number of Prime Divisors of Certain Mersenne Numbers
Math. Comp. v. 21, 1967, p. 700704 

48  D. Shanks & S. Kravitz  On the Distribution of Mersenne Divisors
Math. Comp. v. 21, 1967, p. 97101 

49  B. Tuckerman  The 24th Mersenne Prime
PNAS v. 68, 1971, p. 23192320 
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. 620647 
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), 197879, p. 258261, 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. 13871390 
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. 45 
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. 385397 

58  G. McC. Haworth  Primalitytesting Mersenne Numbers
AAMS v. 4, no. 2, 1983, p. 196, 83T1082 

59  R. P. Brent  New factors of Mersenne numbers, III
AAMS v. 4, no. 2, 1983, p. 197, 83T10138 
Factors M227 
60  G. McC. Haworth  Primalitytesting Mersenne Numbers, II AAMS v. 7, no. 2, 1986, p. 2245, 86T1157 

61  I. Peterson  Priming for a Lucky Strike
Science News v. 133, no. 6, 1988, p. 85 
Missing M110503 found 