Mersenne Bibliography

Mersenne Numbers & Mersenne Primes Bibliography

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.
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.
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: m^n²
Sequence: Entries are ordered by publication date.

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	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	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	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	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	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. 162-165	Wanted List: M157, M167, M193, M199, M227, and M229
8	R. C. Archibald	Mersenne's Numbers Scripta Mathematica v. 3, 1935, p. 112-119	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	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	J. Ferrier	Les nombres premiers, Paris Vuibert (1947), Chapitre IX, Les nombres de Mersenne, p.40-41	See [66] in English.
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	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	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	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	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	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. 128-131	M2203: 59 minutes. M2281: 66 minutes.
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	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	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	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 < 108 in All Mersenne Numbers 2p-1, p Prime < 104 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	J. L. Selfridge & A. Hurwitz	Fermat Numbers and Mersenne Numbers Math. Comp. v. 18, 1964, p. 146-148	Residues 5000 < p < 6000
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 n2\|2n-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	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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