List of Mersenne primes and perfect numbers (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "List of Mersenne primes and perfect numbers" in English language version.

refsWebsite

Global rank English rank

48web.archive.org

1^st place

19doi.org

2^nd place

19mersenne.org

low place

9worldcat.org

5^th place

7utm.edu

1,379^th place

1,175^th place

7jstor.org

26^th place

20^th place

7ams.org

451^st place

277^th place

4books.google.com

3^rd place

3harvard.edu

18^th place

17^th place

2springer.com

274^th place

309^th place

2semanticscholar.org

11^th place

8^th place

2latimes.com

22^nd place

19^th place

2nih.gov

4^th place

2gale.com

1,435^th place

802^nd place

1wikipedia.org

low place

1quantamagazine.org

6,413^th place

4,268^th place

1clarku.edu

6,602^nd place

6,109^th place

1archive.org

6^th place

1st-andrews.ac.uk

1,547^th place

1,410^th place

1digitale-sammlungen.de

958^th place

1,915^th place

1pacific.edu

low place

1biodiversitylibrary.org

387^th place

373^rd place

1bnf.fr

124^th place

544^th place

1nytimes.com

7^th place

1proquest.com

206^th place

124^th place

1ucla.edu

782^nd place

585^th place

1phys.org

1,283^rd place

1,130^th place

1bbc.com

20^th place

30^th place

1slate.com

259^th place

188^th place

1npr.org

92^nd place

72^nd place

ams.org

Wagstaff, Samuel S. (January 1983). "Divisors of Mersenne numbers". Mathematics of Computation. 40 (161): 385–397. doi:10.1090/S0025-5718-1983-0679454-X. ISSN 0025-5718.
Ochem, Pascal; Rao, Michaël (30 January 2012). "Odd perfect numbers are greater than 10¹⁵⁰⁰". Mathematics of Computation. 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718.
"Notes". Mathematics of Computation. 6 (37): 58–61. January 1952. doi:10.1090/S0025-5718-52-99405-2. ISSN 0025-5718. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
"Notes". Mathematics of Computation. 6 (39): 204–205. July 1952. doi:10.1090/S0025-5718-52-99389-7. ISSN 0025-5718.
"Notes". Mathematics of Computation. 7 (41): 67–72. January 1953. doi:10.1090/S0025-5718-53-99372-7. ISSN 0025-5718.
Riesel, Hans (January 1958). "A New Mersenne Prime". Mathematics of Computation. 12 (61): 60. doi:10.1090/S0025-5718-58-99282-2. Archived from the original on 2021-10-28. Retrieved 2021-10-13.
Hurwitz, Alexander (April 1962). "New Mersenne primes". Mathematics of Computation. 16 (78): 249–251. doi:10.1090/S0025-5718-1962-0146162-X. ISSN 0025-5718.

archive.org

Smith, David Eugene (1925). History of Mathematics: Volume II. Dover. p. 21. ISBN 978-0-486-20430-7. {{cite book}}: ISBN / Date incompatibility (help)

bbc.com

"Largest known prime number discovered in Missouri". BBC News. 20 January 2016. Archived from the original on 21 August 2021. Retrieved 13 October 2021.

biodiversitylibrary.org

"Sur un nouveau nombre premier, annoncé par le père Pervouchine" [On a new prime number, announced by Pervouchine]. Bulletin de l'Académie impériale des sciences de St.-Pétersbourg (in French). 31: 532–533. 27 January 1887. Archived from the original on 13 October 2021. Retrieved 13 October 2021 – via Biodiversity Heritage Library.

bnf.fr

visualiseur.bnf.fr

Lucas, Édouard (1876). "Note sur l'application des séries récurrentes à la recherche de la loi de distribution des nombres premiers" [Note on the application of recurrent series to researching the law of prime number distribution]. Comptes rendus de l'Académie des Sciences (in French). 82: 165–167. Archived from the original on 13 October 2021. Retrieved 13 October 2021.

books.google.com

Stillwell, John (2010). Mathematics and Its History. Undergraduate Texts in Mathematics. Springer Science+Business Media. p. 40. ISBN 978-1-4419-6052-8. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
Crilly, Tony (2007). "Perfect numbers". 50 mathematical ideas you really need to know. Quercus Publishing. ISBN 978-1-84724-008-8. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
Dickson, Leonard Eugene (1919). History of the Theory of Numbers, Vol. I. Carnegie Institution of Washington. pp. 4–6. Archived from the original on 2023-04-08. Retrieved 2023-03-19.
Cataldi, Pietro Antonio (1603). Trattato de' numeri perfetti di Pietro Antonio Cataldo [Pietro Antonio Cataldi's treatise on perfect numbers] (in Italian). Presso di Heredi di Giouanni Rossi. Archived from the original on 2023-04-05. Retrieved 2023-03-19.

clarku.edu

mathcs.clarku.edu

Joyce, David E. "Euclid's Elements, Book IX, Proposition 36". mathcs.clarku.edu. Archived from the original on 17 June 2021. Retrieved 13 October 2021.

digitale-sammlungen.de

"'Calendarium ecclesiasticum – BSB Clm 14908'". Bavarian State Library. Archived from the original on 13 October 2021. Retrieved 13 October 2021.

doi.org

Prielipp, Robert W. (1970). "Perfect Numbers, Abundant Numbers, and Deficient Numbers". The Mathematics Teacher. 63 (8): 692–96. doi:10.5951/MT.63.8.0692. JSTOR 27958492. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
Wagstaff, Samuel S. (January 1983). "Divisors of Mersenne numbers". Mathematics of Computation. 40 (161): 385–397. doi:10.1090/S0025-5718-1983-0679454-X. ISSN 0025-5718.
Pomerance, Carl (September 1981). "Recent developments in primality testing" (PDF). The Mathematical Intelligencer. 3 (3): 97–105. doi:10.1007/BF03022861. ISSN 0343-6993. S2CID 121750836.
Ochem, Pascal; Rao, Michaël (30 January 2012). "Odd perfect numbers are greater than 10¹⁵⁰⁰". Mathematics of Computation. 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718.
Powers, R. E. (November 1911). "The Tenth Perfect Number". The American Mathematical Monthly. 18 (11): 195–197. doi:10.2307/2972574. JSTOR 2972574.
"Records of Proceedings at Meetings". Proceedings of the London Mathematical Society. s2-13 (1): iv–xl. 1914. doi:10.1112/plms/s2-13.1.1-s.
"Notes". Mathematics of Computation. 6 (37): 58–61. January 1952. doi:10.1090/S0025-5718-52-99405-2. ISSN 0025-5718. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
"Notes". Mathematics of Computation. 6 (39): 204–205. July 1952. doi:10.1090/S0025-5718-52-99389-7. ISSN 0025-5718.
"Notes". Mathematics of Computation. 7 (41): 67–72. January 1953. doi:10.1090/S0025-5718-53-99372-7. ISSN 0025-5718.
Riesel, Hans (January 1958). "A New Mersenne Prime". Mathematics of Computation. 12 (61): 60. doi:10.1090/S0025-5718-58-99282-2. Archived from the original on 2021-10-28. Retrieved 2021-10-13.
Hurwitz, Alexander (April 1962). "New Mersenne primes". Mathematics of Computation. 16 (78): 249–251. doi:10.1090/S0025-5718-1962-0146162-X. ISSN 0025-5718.
Gillies, Donald B. (January 1964). "Three new Mersenne primes and a statistical theory". Mathematics of Computation. 18 (85): 93–97. doi:10.1090/S0025-5718-1964-0159774-6. JSTOR 2003409.
Tuckerman, Bryant (October 1971). "The 24th Mersenne Prime". Proceedings of the National Academy of Sciences. 68 (10): 2319–2320. Bibcode:1971PNAS...68.2319T. doi:10.1073/pnas.68.10.2319. PMC 389411. PMID 16591945.
Noll, Landon Curt; Nickel, Laura (October 1980). "The 25th and 26th Mersenne primes". Mathematics of Computation. 35 (152): 1387. doi:10.1090/S0025-5718-1980-0583517-4. JSTOR 2006405.
"Announcements". The Mathematical Intelligencer. 5 (1): 60. March 1983. doi:10.1007/BF03023507. ISSN 0343-6993.
Peterson, I. (6 February 1988). "Priming for a Lucky Strike". Science News. 133 (6): 85. doi:10.2307/3972461. JSTOR 3972461.
Colquitt, W. N.; Welsh, L. (April 1991). "A new Mersenne prime". Mathematics of Computation. 56 (194): 867. Bibcode:1991MaCom..56..867C. doi:10.1090/S0025-5718-1991-1068823-9. JSTOR 2008415.
Peterson, I. (28 September 1985). "Prime Time for Supercomputers". Science News. 128 (13): 199. doi:10.2307/3970245. JSTOR 3970245.
Maddox, John (26 March 1992). "The endless search for primality". Nature. 356 (6367): 283. Bibcode:1992Natur.356..283M. doi:10.1038/356283a0. ISSN 1476-4687. S2CID 4327045.

gale.com

go.gale.com

"Largest Known Prime Number Discovered on Cray Research Supercomputer". PR Newswire. 10 January 1994. Archived from the original on 4 November 2021. Retrieved 21 August 2023 – via Gale.

link.gale.com

Gillmor, Dan (3 September 1996). "Crunching numbers: Researchers come up with prime math discovery". Knight Ridder – via Gale.

harvard.edu

ui.adsabs.harvard.edu

Tuckerman, Bryant (October 1971). "The 24th Mersenne Prime". Proceedings of the National Academy of Sciences. 68 (10): 2319–2320. Bibcode:1971PNAS...68.2319T. doi:10.1073/pnas.68.10.2319. PMC 389411. PMID 16591945.
Colquitt, W. N.; Welsh, L. (April 1991). "A new Mersenne prime". Mathematics of Computation. 56 (194): 867. Bibcode:1991MaCom..56..867C. doi:10.1090/S0025-5718-1991-1068823-9. JSTOR 2008415.
Maddox, John (26 March 1992). "The endless search for primality". Nature. 356 (6367): 283. Bibcode:1992Natur.356..283M. doi:10.1038/356283a0. ISSN 1476-4687. S2CID 4327045.

jstor.org

Prielipp, Robert W. (1970). "Perfect Numbers, Abundant Numbers, and Deficient Numbers". The Mathematics Teacher. 63 (8): 692–96. doi:10.5951/MT.63.8.0692. JSTOR 27958492. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
Powers, R. E. (November 1911). "The Tenth Perfect Number". The American Mathematical Monthly. 18 (11): 195–197. doi:10.2307/2972574. JSTOR 2972574.
Gillies, Donald B. (January 1964). "Three new Mersenne primes and a statistical theory". Mathematics of Computation. 18 (85): 93–97. doi:10.1090/S0025-5718-1964-0159774-6. JSTOR 2003409.
Noll, Landon Curt; Nickel, Laura (October 1980). "The 25th and 26th Mersenne primes". Mathematics of Computation. 35 (152): 1387. doi:10.1090/S0025-5718-1980-0583517-4. JSTOR 2006405.
Peterson, I. (6 February 1988). "Priming for a Lucky Strike". Science News. 133 (6): 85. doi:10.2307/3972461. JSTOR 3972461.
Colquitt, W. N.; Welsh, L. (April 1991). "A new Mersenne prime". Mathematics of Computation. 56 (194): 867. Bibcode:1991MaCom..56..867C. doi:10.1090/S0025-5718-1991-1068823-9. JSTOR 2008415.
Peterson, I. (28 September 1985). "Prime Time for Supercomputers". Science News. 128 (13): 199. doi:10.2307/3970245. JSTOR 3970245.

latimes.com

Dembart, Lee (17 September 1985). "Supercomputer Comes Up With Whopping Prime Number". Los Angeles Times. Archived from the original on 2 November 2021. Retrieved 13 October 2021.
Maugh, Thomas H. (27 September 2008). "Rare prime number found". Los Angeles Times. Archived from the original on 27 July 2021. Retrieved 13 October 2021.

mersenne.org

"GIMPS Milestones Report". Great Internet Mersenne Prime Search. Archived from the original on 13 October 2021. Retrieved 31 January 2024.
Sources applying to almost all entries:
- "List of Known Mersenne Prime Numbers". Great Internet Mersenne Prime Search. Archived from the original on 7 June 2020. Retrieved 4 October 2021.
- "GIMPS Discovers 35th Mersenne Prime, 2^1,398,269-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 12 November 1996. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 36th Mersenne Prime, 2^2,976,221-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 1 September 1997. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 37th Mersenne Prime, 2^3,021,377-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 2 February 1998. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 38th Mersenne Prime 2^6,972,593-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 30 June 1999. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 39th Mersenne Prime, 2^13,466,917-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 6 December 2001. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 40th Mersenne Prime, 2^20,996,011-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 2 February 2003. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 41st Mersenne Prime, 2^24,036,583-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 28 May 2004. Archived from the original on 29 January 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 42nd Mersenne Prime, 2^25,964,951-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 27 February 2005. Archived from the original on 14 March 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 43rd Mersenne Prime, 2^30,402,457-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 24 December 2005. Archived from the original on 14 March 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 44th Mersenne Prime, 2^32,582,657-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 11 September 2006. Archived from the original on 26 January 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 45th and 46th Mersenne Primes, 2^43,112,609-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 15 September 2008. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 47th Mersenne Prime". Great Internet Mersenne Prime Search. 12 April 2009. Archived from the original on 19 February 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 48th Mersenne Prime, 2^57,885,161-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 5 February 2013. Archived from the original on 26 January 2021. Retrieved 13 October 2021.
- "GIMPS Project Discovers Largest Known Prime Number: 2^74,207,281-1". Great Internet Mersenne Prime Search. 19 January 2016. Archived from the original on 7 January 2018. Retrieved 13 October 2021.
- "GIMPS Project Discovers Largest Known Prime Number: 2^77,232,917-1". Great Internet Mersenne Prime Search. 3 January 2018. Archived from the original on 4 January 2018. Retrieved 13 October 2021.
- "GIMPS Discovers Largest Known Prime Number: 2^82,589,933-1". Great Internet Mersenne Prime Search. 21 December 2018. Archived from the original on 22 December 2018. Retrieved 13 October 2021.
- "GIMPS Discovers Largest Known Prime Number: 2^136,279,841-1". Great Internet Mersenne Prime Search. 21 October 2024. Retrieved 21 October 2024.

nih.gov

ncbi.nlm.nih.gov

Tuckerman, Bryant (October 1971). "The 24th Mersenne Prime". Proceedings of the National Academy of Sciences. 68 (10): 2319–2320. Bibcode:1971PNAS...68.2319T. doi:10.1073/pnas.68.10.2319. PMC 389411. PMID 16591945.

pubmed.ncbi.nlm.nih.gov

Tuckerman, Bryant (October 1971). "The 24th Mersenne Prime". Proceedings of the National Academy of Sciences. 68 (10): 2319–2320. Bibcode:1971PNAS...68.2319T. doi:10.1073/pnas.68.10.2319. PMC 389411. PMID 16591945.

npr.org

Palca, Joe (21 December 2018). "The World Has A New Largest-Known Prime Number". NPR. Archived from the original on 30 July 2021. Retrieved 13 October 2021.

nytimes.com

"Science Watch: A New Prime Number". The New York Times. 5 June 1979. Archived from the original on 2 November 2021. Retrieved 13 October 2021.

pacific.edu

scholarlycommons.pacific.edu

Euler, Leonhard (1772). "Extrait d'un lettre de M. Euler le pere à M. Bernoulli concernant le Mémoire imprimé parmi ceux de 1771, p 318" [Extract of a letter from Mr. Euler to Mr. Bernoulli, concerning the Mémoire published among those of 1771]. Nouveaux Mémoires de l'académie royale des sciences de Berlin (in French). 1772: 35–36. Archived from the original on 15 August 2020. Retrieved 13 October 2021 – via Euler Archive.

phys.org

Yirka, Bob (6 February 2013). "University professor discovers largest prime number to date". phys.org. Archived from the original on 16 January 2021. Retrieved 13 October 2021.

proquest.com

"Number is largest prime found yet". The Globe and Mail. 24 September 1983. ProQuest 386439660. Archived from the original on 2 November 2021. Retrieved 7 January 2022 – via ProQuest.

quantamagazine.org

Nadis, Steve (10 September 2020). "Mathematicians Open a New Front on an Ancient Number Problem". Quanta Magazine. Like many of his 21st-century peers, Nielsen thinks there probably aren't any OPNs. And, also like his peers, he does not believe a proof is within immediate reach.

semanticscholar.org

api.semanticscholar.org

Pomerance, Carl (September 1981). "Recent developments in primality testing" (PDF). The Mathematical Intelligencer. 3 (3): 97–105. doi:10.1007/BF03022861. ISSN 0343-6993. S2CID 121750836.
Maddox, John (26 March 1992). "The endless search for primality". Nature. 356 (6367): 283. Bibcode:1992Natur.356..283M. doi:10.1038/356283a0. ISSN 1476-4687. S2CID 4327045.

slate.com

Lamb, Evelyn (4 January 2018). "Why You Should Care About a Prime Number That's 23,249,425 Digits Long". Slate Magazine. Archived from the original on 9 October 2021. Retrieved 13 October 2021.

springer.com

link.springer.com

Pomerance, Carl (September 1981). "Recent developments in primality testing" (PDF). The Mathematical Intelligencer. 3 (3): 97–105. doi:10.1007/BF03022861. ISSN 0343-6993. S2CID 121750836.
"Announcements". The Mathematical Intelligencer. 5 (1): 60. March 1983. doi:10.1007/BF03023507. ISSN 0343-6993.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F. "Perfect numbers". MacTutor History of Mathematics archive. Archived from the original on 5 October 2021. Retrieved 13 October 2021.

ucla.edu

math.ucla.edu

Smith, Edson. "The UCLA Mersenne Prime". UCLA Mathematics. Archived from the original on 22 November 2021. Retrieved 22 November 2021.

utm.edu

primes.utm.edu

Caldwell, Chris K. "Mersenne Primes: History, Theorems and Lists". PrimePages. Archived from the original on 4 October 2021. Retrieved 4 October 2021.
Caldwell, Chris K. "If 2ⁿ-1 is prime, then so is n". PrimePages. Archived from the original on 5 October 2021. Retrieved 12 October 2021.
Caldwell, Chris K. "Characterizing all even perfect numbers". PrimePages. Archived from the original on 8 October 2014. Retrieved 12 October 2021.
Caldwell, Chris K. "Heuristics Model for the Distribution of Mersennes". PrimePages. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "The Largest Known prime by Year: A Brief History". PrimePages. Archived from the original on 4 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "Modular restrictions on Mersenne divisors". PrimePages. Archived from the original on 11 November 2021. Retrieved 22 November 2021.
Caldwell, Chris K. "A Prime of Record Size! 2^1257787-1". PrimePages. Archived from the original on 5 October 2021. Retrieved 13 October 2021.

web.archive.org

Stillwell, John (2010). Mathematics and Its History. Undergraduate Texts in Mathematics. Springer Science+Business Media. p. 40. ISBN 978-1-4419-6052-8. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "Mersenne Primes: History, Theorems and Lists". PrimePages. Archived from the original on 4 October 2021. Retrieved 4 October 2021.
Caldwell, Chris K. "If 2ⁿ-1 is prime, then so is n". PrimePages. Archived from the original on 5 October 2021. Retrieved 12 October 2021.
Prielipp, Robert W. (1970). "Perfect Numbers, Abundant Numbers, and Deficient Numbers". The Mathematics Teacher. 63 (8): 692–96. doi:10.5951/MT.63.8.0692. JSTOR 27958492. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "Characterizing all even perfect numbers". PrimePages. Archived from the original on 8 October 2014. Retrieved 12 October 2021.
Crilly, Tony (2007). "Perfect numbers". 50 mathematical ideas you really need to know. Quercus Publishing. ISBN 978-1-84724-008-8. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "Heuristics Model for the Distribution of Mersennes". PrimePages. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
Caldwell, Chris K. "The Largest Known prime by Year: A Brief History". PrimePages. Archived from the original on 4 October 2021. Retrieved 13 October 2021.
"GIMPS Milestones Report". Great Internet Mersenne Prime Search. Archived from the original on 13 October 2021. Retrieved 31 January 2024.
Sources applying to almost all entries:
- "List of Known Mersenne Prime Numbers". Great Internet Mersenne Prime Search. Archived from the original on 7 June 2020. Retrieved 4 October 2021.
- Joyce, David E. "Euclid's Elements, Book IX, Proposition 36". mathcs.clarku.edu. Archived from the original on 17 June 2021. Retrieved 13 October 2021.
- Dickson, Leonard Eugene (1919). History of the Theory of Numbers, Vol. I. Carnegie Institution of Washington. pp. 4–6. Archived from the original on 2023-04-08. Retrieved 2023-03-19.
- O'Connor, John J.; Robertson, Edmund F. "Perfect numbers". MacTutor History of Mathematics archive. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
- "'Calendarium ecclesiasticum – BSB Clm 14908'". Bavarian State Library. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
- Cataldi, Pietro Antonio (1603). Trattato de' numeri perfetti di Pietro Antonio Cataldo [Pietro Antonio Cataldi's treatise on perfect numbers] (in Italian). Presso di Heredi di Giouanni Rossi. Archived from the original on 2023-04-05. Retrieved 2023-03-19.
- Caldwell, Chris K. "Modular restrictions on Mersenne divisors". PrimePages. Archived from the original on 11 November 2021. Retrieved 22 November 2021.
- Euler, Leonhard (1772). "Extrait d'un lettre de M. Euler le pere à M. Bernoulli concernant le Mémoire imprimé parmi ceux de 1771, p 318" [Extract of a letter from Mr. Euler to Mr. Bernoulli, concerning the Mémoire published among those of 1771]. Nouveaux Mémoires de l'académie royale des sciences de Berlin (in French). 1772: 35–36. Archived from the original on 15 August 2020. Retrieved 13 October 2021 – via Euler Archive.
- "Sur un nouveau nombre premier, annoncé par le père Pervouchine" [On a new prime number, announced by Pervouchine]. Bulletin de l'Académie impériale des sciences de St.-Pétersbourg (in French). 31: 532–533. 27 January 1887. Archived from the original on 13 October 2021. Retrieved 13 October 2021 – via Biodiversity Heritage Library.
- Lucas, Édouard (1876). "Note sur l'application des séries récurrentes à la recherche de la loi de distribution des nombres premiers" [Note on the application of recurrent series to researching the law of prime number distribution]. Comptes rendus de l'Académie des Sciences (in French). 82: 165–167. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
- "Notes". Mathematics of Computation. 6 (37): 58–61. January 1952. doi:10.1090/S0025-5718-52-99405-2. ISSN 0025-5718. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
- Riesel, Hans (January 1958). "A New Mersenne Prime". Mathematics of Computation. 12 (61): 60. doi:10.1090/S0025-5718-58-99282-2. Archived from the original on 2021-10-28. Retrieved 2021-10-13.
- "Science Watch: A New Prime Number". The New York Times. 5 June 1979. Archived from the original on 2 November 2021. Retrieved 13 October 2021.
- "Number is largest prime found yet". The Globe and Mail. 24 September 1983. ProQuest 386439660. Archived from the original on 2 November 2021. Retrieved 7 January 2022 – via ProQuest.
- Dembart, Lee (17 September 1985). "Supercomputer Comes Up With Whopping Prime Number". Los Angeles Times. Archived from the original on 2 November 2021. Retrieved 13 October 2021.
- "Largest Known Prime Number Discovered on Cray Research Supercomputer". PR Newswire. 10 January 1994. Archived from the original on 4 November 2021. Retrieved 21 August 2023 – via Gale.
- Caldwell, Chris K. "A Prime of Record Size! 2^1257787-1". PrimePages. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 35th Mersenne Prime, 2^1,398,269-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 12 November 1996. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 36th Mersenne Prime, 2^2,976,221-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 1 September 1997. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 37th Mersenne Prime, 2^3,021,377-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 2 February 1998. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 38th Mersenne Prime 2^6,972,593-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 30 June 1999. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 39th Mersenne Prime, 2^13,466,917-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 6 December 2001. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 40th Mersenne Prime, 2^20,996,011-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 2 February 2003. Archived from the original on 7 June 2020. Retrieved 13 October 2021.
- "GIMPS Discovers 41st Mersenne Prime, 2^24,036,583-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 28 May 2004. Archived from the original on 29 January 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 42nd Mersenne Prime, 2^25,964,951-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 27 February 2005. Archived from the original on 14 March 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 43rd Mersenne Prime, 2^30,402,457-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 24 December 2005. Archived from the original on 14 March 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 44th Mersenne Prime, 2^32,582,657-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 11 September 2006. Archived from the original on 26 January 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 45th and 46th Mersenne Primes, 2^43,112,609-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 15 September 2008. Archived from the original on 5 October 2021. Retrieved 13 October 2021.
- "GIMPS Discovers 47th Mersenne Prime". Great Internet Mersenne Prime Search. 12 April 2009. Archived from the original on 19 February 2021. Retrieved 13 October 2021.
- Maugh, Thomas H. (27 September 2008). "Rare prime number found". Los Angeles Times. Archived from the original on 27 July 2021. Retrieved 13 October 2021.
- Smith, Edson. "The UCLA Mersenne Prime". UCLA Mathematics. Archived from the original on 22 November 2021. Retrieved 22 November 2021.
- "GIMPS Discovers 48th Mersenne Prime, 2^57,885,161-1 is now the Largest Known Prime". Great Internet Mersenne Prime Search. 5 February 2013. Archived from the original on 26 January 2021. Retrieved 13 October 2021.
- Yirka, Bob (6 February 2013). "University professor discovers largest prime number to date". phys.org. Archived from the original on 16 January 2021. Retrieved 13 October 2021.
- "GIMPS Project Discovers Largest Known Prime Number: 2^74,207,281-1". Great Internet Mersenne Prime Search. 19 January 2016. Archived from the original on 7 January 2018. Retrieved 13 October 2021.
- "Largest known prime number discovered in Missouri". BBC News. 20 January 2016. Archived from the original on 21 August 2021. Retrieved 13 October 2021.
- "GIMPS Project Discovers Largest Known Prime Number: 2^77,232,917-1". Great Internet Mersenne Prime Search. 3 January 2018. Archived from the original on 4 January 2018. Retrieved 13 October 2021.
- Lamb, Evelyn (4 January 2018). "Why You Should Care About a Prime Number That's 23,249,425 Digits Long". Slate Magazine. Archived from the original on 9 October 2021. Retrieved 13 October 2021.
- "GIMPS Discovers Largest Known Prime Number: 2^82,589,933-1". Great Internet Mersenne Prime Search. 21 December 2018. Archived from the original on 22 December 2018. Retrieved 13 October 2021.
- Palca, Joe (21 December 2018). "The World Has A New Largest-Known Prime Number". NPR. Archived from the original on 30 July 2021. Retrieved 13 October 2021.

wikipedia.org

en.wikipedia.org

As of 14 May 2025^[update].^[13] All exponents below the lowest unverified milestone have been checked more than once. All exponents below the lowest untested milestone have been checked at least once.

worldcat.org

search.worldcat.org

Wagstaff, Samuel S. (January 1983). "Divisors of Mersenne numbers". Mathematics of Computation. 40 (161): 385–397. doi:10.1090/S0025-5718-1983-0679454-X. ISSN 0025-5718.
Pomerance, Carl (September 1981). "Recent developments in primality testing" (PDF). The Mathematical Intelligencer. 3 (3): 97–105. doi:10.1007/BF03022861. ISSN 0343-6993. S2CID 121750836.
Ochem, Pascal; Rao, Michaël (30 January 2012). "Odd perfect numbers are greater than 10¹⁵⁰⁰". Mathematics of Computation. 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718.
"Notes". Mathematics of Computation. 6 (37): 58–61. January 1952. doi:10.1090/S0025-5718-52-99405-2. ISSN 0025-5718. Archived from the original on 13 October 2021. Retrieved 13 October 2021.
"Notes". Mathematics of Computation. 6 (39): 204–205. July 1952. doi:10.1090/S0025-5718-52-99389-7. ISSN 0025-5718.
"Notes". Mathematics of Computation. 7 (41): 67–72. January 1953. doi:10.1090/S0025-5718-53-99372-7. ISSN 0025-5718.
Hurwitz, Alexander (April 1962). "New Mersenne primes". Mathematics of Computation. 16 (78): 249–251. doi:10.1090/S0025-5718-1962-0146162-X. ISSN 0025-5718.
"Announcements". The Mathematical Intelligencer. 5 (1): 60. March 1983. doi:10.1007/BF03023507. ISSN 0343-6993.
Maddox, John (26 March 1992). "The endless search for primality". Nature. 356 (6367): 283. Bibcode:1992Natur.356..283M. doi:10.1038/356283a0. ISSN 1476-4687. S2CID 4327045.