# Bibliography

## Bibliography pertinent to discoverers of record prime gaps

 Torbjörn Alm. Jens Kruse Andersen. See also Andersen's The Top-20 Prime Gaps, the successor to a compilation maintained until February 2004 by Paul Leyland. Andersen's work has also confirmed the certification of a great many probabilistic gaps, as well as the probabilistic validity of many questionable gaps of thousands of digits. Kenneth I. Appel and J. Barkley Rosser, “Table for estimating functions of primes,” Communications Research Division Technical Report Number 4, Institute for Defense Analyses, Princeton NJ (1961), xxxii + 125 pp. (22 cm.). Reviewed in Math. Comp. 16:80 (1962) 500-501 RMT 55. C. L. Baker and F. J. Gruenberger, “The first six million prime numbers,” The Rand Corporation, Santa Monica CA, published by the Microcard Foundation, Madison WI (1959), 8 pp. (16x23 cm.) + 62 cards (7.5x12.6 cm). Reviewed in Math. Comp. 15:73 (1961) 82 RMT 4. D. Baugh and F. O'Hara, Letters to the Editor, “Large prime gaps” and “And more,” J. Recreational Math. 24:3 (1992) 186-187. Richard P. Brent, “The first occurrence of large gaps between successive primes,” Math. Comp. 27:124 (1973) 959-963, MR 48#8360. Richard P. Brent, “The first occurrence of certain large prime gaps,” Math. Comp. 35:152 (1980) 1435-36, MR 81g:10002. Kenneth Conrow . Harvey Dubner and Harry Nelson, “Seven consecutive primes in arithmetic progression,” Math. Comp. 66 (1997) 1743-1749, MR 98a:11122. Dubner wrote (ca. 1995-96) codes implementing the methods discussed in this paper, and these formed the basis for the codes written by Dubner and Nicely and used in their discoveries of first known occurrence prime gaps (exceeding 1065). Patrick De Geest. J. W. L. Glaisher, “On long successions of composite numbers,” Messenger of Mathematics 7 (1877) 102-106, 171-176. F. J. Gruenberger and G. Armerding, “Statistics on the first six million prime numbers,” Paper P-2460 of the Rand Corporation, Santa Monica CA (1961), 145 pp. (8.5" x 11"). Reviewed in Math. Comp. 19:91 (1965) 503-505 RMT 73. Siegfried "Zig" Herzog, Mont Alto campus of Penn State University. Yûji Kida, Professor of Mathematics, Rikkyo University, Japan, author of UBASIC, a freeware ultraprecision programming, development, and runtime environment with number theoretical enhancements. Professor Donald Ervin Knuth, Stanford University. L. J. Lander and Thomas R. Parkin, “On the first appearance of prime differences,” Math. Comp. 21 (1967) 483-488, MR 37#6237. Derrick Henry Lehmer, “Tables concerning the distribution of primes up to 37 millions” (1957). Copy deposited in the UMT file and reviewed in MTAC 13 (1959) 56-57 RMT 3. Paul Leyland, The Top-20 Prime Gaps, maintained by Jens Kruse Andersen since February 2004. François Morain, deterministic certification of certain primes, using his own implementations of ECPP (elliptic curve primality proving). Thomas R. Nicely, “New maximal prime gaps and first occurrences”, Math. Comp. 68:227 (July, 1999) 1311-1315, MR 99i:11004. Thomas R. Nicely and Bertil Nyman, “First occurrence of a prime gap of 1000 or greater,” unpublished (26 May 1999). NoAttrib, anonymous contributors who do not wish attribution. Bertil Nyman and Thomas R. Nicely, “New prime gaps between $10^{15}$ and $5 \times 10^{16}$,” Journal of Integer Sequences 6 (2003), Article 03.3.1, 6 pp. (electronic). Available in various formats (PS, PDF, dvi, AMS-LaTeX2e) at the home page of the Journal of Integer Sequences. Paulo Ribenboim, “The little book of big primes,” Springer-Verlag, New York, 1991, MR 92i:11008. Ribenboim documents (p. 142) Young and Potler's otherwise unpublished discovery (probably in 1988) of the 804 gap. PGS, the Prime Gap Searches project at the Mersenne Forum. S. Cole, L. Desnogues, R. Gerbicz, D. Jacobsen, A.P. Key, Jerry LaGrou, L. Morelli, A. Nair, C.E.L. Pinho, M. Raab, T. Ritschel, R. Ruiz-Huidobro, R.W. Smith (coordinator), D. Stevens. Computer codes in C and Perl, developed by Robert Gerbicz, Dana Jacobsen, Antonio P. Key, et al. Project initiated April 2017. Luis Rodriguez (AKA Luis Rodriguez Abreu/Torres), e-mail communications (15/18 January 1999) to Dr. Thomas R Nicely. Hans Rosenthal. Tomás Oliveira e Silva, Universidade de Aveiro, Portugal. Research project in progress, concerning numerical verification of the Goldbach conjecture to a large upper bound, with collateral counts of primes, twin primes, and prime gaps. Robert W. Smith, coordinator of the Prime Gap Searches project at the Mersenne Forum. A. E. Western, "Note on the magnitude of the difference between successive primes," J. London Math. Soc. 9 (1934) 276-278. Marek Wolf, “Unexpected regularities in the distribution of prime numbers”, (preprint, May 1996). Marek Wolf, “First occurrence of a given gap between consecutive primes”, (preprint, April 1997). Jeff Young and Aaron Potler, “First occurrence prime gaps,” Math. Comp. 52:185 (1989) 221-224, MR 89f:11019.