„Mersenne-prímek” változatai közötti eltérés

See also Mémoires de l'Académie impériale des sciences de St.-Pétersbourg: Sciences mathématiques, physiques et naturelles, vol. 48

</ref>

| [[Lucas sequence]]s

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| style="text-align:right;"| 157

| 1952. január 30.<ref name="autogenerated4">"Using the standard Lucas test for Mersenne primes as programmed by R. M. Robinson, the SWAC has discovered the primes 2⁵²¹&nbsp;−&nbsp;1 and 2⁶⁰⁷&nbsp;−&nbsp;1 on January 30, 1952." D. H. Lehmer, ''Recent Discoveries of Large Primes'', Mathematics of Computation, vol. 6, No. 37 (1952), p. 61, http://www.ams.org/journals/mcom/1952-06-037/S0025-5718-52-99404-0/S0025-5718-52-99404-0.pdf [Retrieved 2012-09-18]</ref>

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| style="text-align:right;"| 14

| style="text-align:right;"| 183

| 1952. január 30.<ref name="autogenerated4" />

| LLT / SWAC

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| style="text-align:right;"| 386

| 1952. június 25.<ref>"The program described in Note 131 (c) has produced the 15th Mersenne prime 2¹²⁷⁹&nbsp;−&nbsp;1 on June 25. The SWAC tests this number in 13 minutes and 25 seconds." D. H. Lehmer, ''A New Mersenne Prime'', Mathematics of Computation, vol. 6, No. 39 (1952), p. 205, http://www.ams.org/journals/mcom/1952-06-039/S0025-5718-52-99387-3/S0025-5718-52-99387-3.pdf [Retrieved 2012-09-18]</ref>

| LLT / SWAC

|-

| style="text-align:right;"| 664

| 1952. október 7.<ref name="autogenerated2">"Two more Mersenne primes, 2²²⁰³&nbsp;−&nbsp;1 and 2²²⁸¹&nbsp;−&nbsp;1, were discovered by the SWAC on October 7 and 9, 1952." D. H. Lehmer, ''Two New Mersenne Primes'', Mathematics of Computation, vol. 7, No. 41 (1952), p. 72, http://www.ams.org/journals/mcom/1953-07-041/S0025-5718-53-99371-5/S0025-5718-53-99371-5.pdf [Retrieved 2012-09-18]</ref>

| LLT / SWAC

|-

| style="text-align:right;"| 687

| 1952. október 9.<ref name="autogenerated2" />

| LLT / SWAC

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| style="text-align:right;"| {{szám|1281}}

| 1961. november 3.<ref name="Hurwitz and Selfridge 1961">A. Hurwitz and J. L. Selfridge, ''Fermat numbers and perfect numbers'', Notices of the American Mathematical Society, v. 8, 1961, p. 601, abstract 587-104.</ref><ref name="autogenerated5">"If {{math|''p''}} is prime, {{math|''M_p'' {{=}} 2^''p'' − 1}} is called a Mersenne number. The primes {{math|''M''₄₂₅₃}} and {{math|''M''₄₄₂₃}} were discovered by coding the Lucas-Lehmer test for the IBM 7090." Alexander Hurwitz, ''New Mersenne Primes'', Mathematics of Computation, vol. 16, No. 78 (1962), pp. 249–251, http://www.ams.org/journals/mcom/1962-16-078/S0025-5718-1962-0146162-X/S0025-5718-1962-0146162-X.pdf [Retrieved 2012-09-18]</ref>

| LLT / [[IBM 7090]]

|-

| style="text-align:right;"| {{szám|2917}}

| 1963. május 11.<ref name="autogenerated3">"The primes {{math|''M''₉₆₈₉}}, {{math|''M''₉₉₄₁}}, and {{math|''M''₁₁₂₁₃}} which are now the largest known primes, were discovered by Illiac II at the Digital Computer Laboratory of the University of Illinois." Donald B. Gillies, ''Three New Mersenne Primes and a Statistical Theory'', Mathematics of Computation, vol. 18, No. 85 (1964), pp. 93–97, http://www.ams.org/journals/mcom/1964-18-085/S0025-5718-1964-0159774-6/S0025-5718-1964-0159774-6.pdf [Retrieved 2012-09-18]</ref>

| LLT / [[ILLIAC II]]

|-

| style="text-align:right;"| 2,993

| 1963. május 16.<ref name="autogenerated3" />

| LLT / ILLIAC II

|-

| style="text-align:right;"| {{szám|3376}}

| 1963. június 2.<ref name="autogenerated3" />

| LLT / ILLIAC II

|-

| style="text-align:right;"| {{szám|6533}}

| 1978. október 30.<ref>"On October 30, 1978 at 9:40 pm, we found {{math|''M''₂₁₇₀₁}} to be prime. The CPU time required for this test was 7:40:20. Tuckerman and Lehmer later provided confirmation of this result." Curt Noll and Laura Nickel, ''The 25th and 26th Mersenne Primes'', Mathematics of Computation, vol. 35, No. 152 (1980), pp. 1387–1390, http://www.ams.org/journals/mcom/1980-35-152/S0025-5718-1980-0583517-4/S0025-5718-1980-0583517-4.pdf [Retrieved 2012-09-18]</ref>

| LLT / [[CDC Cyber]] 174

|-

| style="text-align:right;"| {{szám|13395}}

| 1979. április 8.<ref>David Slowinski, "Searching for the 27th Mersenne Prime", ''Journal of Recreational Mathematics'', v. 11(4), 1978–79, pp. 258–261, MR 80g #10013</ref><ref>"The 27th Mersenne prime. It has 13395 digits and equals 2⁴⁴⁴⁹⁷&nbsp;–&nbsp;1. [...] Its primeness was determined on April 8, 1979 using the Lucas–Lehmer test. The test was programmed on a CRAY-1 computer by David Slowinski & Harry Nelson." (p. 15) "The result was that after applying the Lucas–Lehmer test to about a thousand numbers, the code determined, on Sunday, April 8th, that 2⁴⁴⁴⁹⁷&nbsp;−&nbsp;1 is, in fact, the 27th Mersenne prime." (p. 17), David Slowinski, "Searching for the 27th Mersenne Prime", ''Cray Channels'', vol. 4, no. 1, (1982), pp. 15–17.</ref>

| LLT / [[Cray 1]]

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| style="text-align:right;"| {{szám|33265}}

| 1988. január 29.<ref>"An FFT containing 8192 complex elements, which was the minimum size required to test M₁₁₀₅₀₃, ran approximately 11 minutes on the SX-2. The discovery of {{math|''M''₁₁₀₅₀₃}} (January 29, 1988) has been confirmed." W. N. Colquitt and L. Welsh, Jr., ''A New Mersenne Prime'', Mathematics of Computation, vol. 56, No. 194 (April 1991), pp. 867–870, http://www.ams.org/journals/mcom/1991-56-194/S0025-5718-1991-1068823-9/S0025-5718-1991-1068823-9.pdf [Retrieved 2012-09-18]</ref><ref>"This week, two computer experts found the 31st Mersenne prime. But to their surprise, the newly discovered prime number falls between two previously known Mersenne primes. It occurs when {{math|''p'' {{=}} 110,503}}, making it the third-largest Mersenne prime known." I. Peterson, ''Priming for a lucky strike'' Science News; 2/6/88, Vol. 133 Issue 6, pp. 85–85. http://ehis.ebscohost.com/ehost/detail?vid=3&hid=23&sid=9a9d7493-ffed-410b-9b59-b86c63a93bc4%40sessionmgr10&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=afh&AN=8824187 [Retrieved 2012-09-18]</ref>

| LLT / [[NEC SX architecture|NEC SX-2]]<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/mersenne.html |title=Mersenne Prime Numbers |publisher=Omes.uni-bielefeld.de |date=2011-01-05 |accessdate=2011-05-21}}</ref>

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| style="text-align:right;"| {{szám|7816230}}

| 2005. február 18.

| LLT / Prime95 on 2.4&nbsp;GHz Pentium 4

|-

| style="text-align:right;"| {{szám|9152052}}

| 2005. december 15.

| LLT / Prime95 on 2&nbsp;GHz Pentium 4

|-

| style="text-align:right;"| {{szám|11185272}}

| 2008. szeptember 6.

| LLT / Prime95 on 2.83&nbsp;GHz [[Core 2 Duo]]

|-

| style="text-align:right;"| {{szám|12978189}}

| 2008. augusztus 23.

| LLT / Prime95 on [[Dell Optiplex]] 745

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| style="text-align:right;"| {{szám|23249425}}

| 2017. december 26.

| LLT / Prime95 on 3.3 GHz Intel [[Core i5-6600]]<ref>{{cite web|url=https://www.mersenne.org/primes/|title=List of known Mersenne prime numbers|accessdate=3 January 2018}}</ref>

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