Distributed primality proving and the primality of (23539 + 1)/3

François Morain

doi:10.1007/3-540-46877-3_10

Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3

François Morain

IGFL, Université de Lyon, Université Lyon 1

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the 1065-digit (2³⁵³⁹+1)/3, the first ordinary Titanic prime.

Original language	English
Title of host publication	Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings
Editors	Ivan Bjerre Damgard
Publisher	Springer Verlag
Pages	110-123
Number of pages	14
ISBN (Print)	9783540535874
DOIs	https://doi.org/10.1007/3-540-46877-3_10
Publication status	Published - 1 Jan 1991
Event	Conference on the Theory and Application of Cryptology, 1990 - Aarhus, Denmark Duration: 21 May 1990 → 24 May 1990

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	473 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Conference on the Theory and Application of Cryptology, 1990
Country/Territory	Denmark
City	Aarhus
Period	21/05/90 → 24/05/90

Access to Document

10.1007/3-540-46877-3_10

Cite this

Morain, F. (1991). Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3. In I. B. Damgard (Ed.), Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings (pp. 110-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 473 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-46877-3_10

Morain, François. / Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3. Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. editor / Ivan Bjerre Damgard. Springer Verlag, 1991. pp. 110-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the 1065-digit (23539+1)/3, the first ordinary Titanic prime.",

author = "Fran{\c c}ois Morain",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1991.; Conference on the Theory and Application of Cryptology, 1990 ; Conference date: 21-05-1990 Through 24-05-1990",

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Morain, F 1991, Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3. in IB Damgard (ed.), Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 473 LNCS, Springer Verlag, pp. 110-123, Conference on the Theory and Application of Cryptology, 1990, Aarhus, Denmark, 21/05/90. https://doi.org/10.1007/3-540-46877-3_10

Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3. / Morain, François.
Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. ed. / Ivan Bjerre Damgard. Springer Verlag, 1991. p. 110-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 473 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We explain how the Elliptic Curve Primality Proving algorithm can be implemented in a distributed way. Applications are given to the certification of large primes (more than 500 digits). As a result, we describe the successful attempt at proving the primality of the 1065-digit (23539+1)/3, the first ordinary Titanic prime.

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Morain F. Distributed primality proving and the primality of (2³⁵³⁹ + 1)/3. In Damgard IB, editor, Advances in Cryptology — EUROCRYPT 1990 - Workshop on the Theory and Application of Cryptographic Techniques, Proceedings. Springer Verlag. 1991. p. 110-123. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/3-540-46877-3_10