Found 48th Mersenne prime
Mathematicians from the distributed GIMPS primer search project announced the discovery of a new Mersenne prime number . This is an important event for the mathematical community, because until now only 47 such numbers were known, the latter was found in June 2009.
The 48th Mersenne prime is 2 57.885.161 -1, with 17.425.170 decimal places. See the full number in text format .
Mersenne numbers are of the form 2 n -1, where n is a positive integer. Mersenne primes are the largest primes known to science. The previous world record belonged to the number 2 43.112.609 -1, which has 12.978.189 decimal places.
Distributed project on finding prime numbers GIMPS was launched in 1997, and is now considered the longest continuous process of distributed computing in the history of mankind: it has been going on for almost 17 years. Now, at peak times, 360,000 processors are involved in GIMPS with a total capacity of 150 trillion operations per second.
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During the work of GIMPS, participants in this project found 14 Mersenne primes. The last of them, 2 57.885.161 -1, was discovered on January 25, 2013 at 23:30:26 UTC, after which it was rechecked several times on different hardware and software. In particular, the MLucas program checked the 48th Mersenne prime number for six days on a 32-core server, and confirmed it. On Nvidia GPU in the CUDALucas program , the number was checked in 3.6 days and also confirmed it.
GIMPS software developers and project participants have already shared a $ 100,000 over the past Mersenn prime number with at least 10 million decimal places. The next prize is $ 150,000 for a number with at least 100 million decimal places. For the number just found will give only $ 3000 .
In the list of the largest prime numbers known to date, ten first places are occupied by the numbers of Mersenne.
Cataldi, Descartes, Fermat, Mersenne, Leibniz, Euler, and many other mathematicians fought over the search for the largest possible prime numbers. In the course of solving this riddle, many sections of number theory were developed (for example, Fermat's small theorem and the quadratic law of reciprocity). In the 20th century, this search led to the creation of new fast ways to multiply integers: in 1968, mathematician Folker Strassen figured out how to use the fast Fourier transform for this. Now this method is known as the Strassen algorithm, its improved version is used in the GIMPS software and everywhere for the rapid multiplication of matrices.
The mystery of Mersenne's primes and the search for new primes have instilled a love for mathematics in many schoolchildren, who as a result chose a scientific and engineering career for themselves.
In general, the search for new prime numbers, and especially Mersenne numbers, can be compared to collecting rare things.
The 48th Mersenne prime is 2 57.885.161 -1, with 17.425.170 decimal places. See the full number in text format .
Mersenne numbers are of the form 2 n -1, where n is a positive integer. Mersenne primes are the largest primes known to science. The previous world record belonged to the number 2 43.112.609 -1, which has 12.978.189 decimal places.
Distributed project on finding prime numbers GIMPS was launched in 1997, and is now considered the longest continuous process of distributed computing in the history of mankind: it has been going on for almost 17 years. Now, at peak times, 360,000 processors are involved in GIMPS with a total capacity of 150 trillion operations per second.
')
During the work of GIMPS, participants in this project found 14 Mersenne primes. The last of them, 2 57.885.161 -1, was discovered on January 25, 2013 at 23:30:26 UTC, after which it was rechecked several times on different hardware and software. In particular, the MLucas program checked the 48th Mersenne prime number for six days on a 32-core server, and confirmed it. On Nvidia GPU in the CUDALucas program , the number was checked in 3.6 days and also confirmed it.
GIMPS software developers and project participants have already shared a $ 100,000 over the past Mersenn prime number with at least 10 million decimal places. The next prize is $ 150,000 for a number with at least 100 million decimal places. For the number just found will give only $ 3000 .
In the list of the largest prime numbers known to date, ten first places are occupied by the numbers of Mersenne.
Top 100
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Place Description Discharges Who Year Description
----- ---------------------------- ------- ----- ---- - -------------
1 2 ^ 57885161-1 17425170 G13 2013 Mersenn 48 ??
2 2 ^ 43112609-1 12978189 G10 2008 Mersenn 47 ??
3 2 ^ 42643801-1 12837064 G12 2009 Mersenn 46 ??
4 2 ^ 37156667-1 11185272 G11 2008 Mersenn 45?
5 2 ^ 32582657-1 9808358 G9 2006 Mersenn 44?
6 2 ^ 30402457-1 9152052 G9 2005 Mersenn 43?
7 2 ^ 25964951-1 7816230 G8 2005 Mersenn 42
8 2 ^ 24036583-1 7235733 G7 2004 Mersenn 41
9 2 ^ 20996011-1 6320430 G6 2003 Mersenn 40
10 2 ^ 13466917-1 4053946 G5 2001 Mersenn 39
11 19249 * 2 ^ 13018586 + 1 3918990 SB10 2007
12 475856 ^ 524288 + 1 2976633 L3230 2012 Generalized Farm
13 356926 ^ 524288 + 1 2911151 L3209 2012 Generalized Farm
14 341112 ^ 524288 + 1 2900832 L3184 2012 Generalized Farm
15 27653 * 2 ^ 9167433 + 1 2759677 SB8 2005
16 90527 * 2 ^ 9162167 + 1 2758093 L1460 2010
17 75898 ^ 524288 + 1 2558647 p334 2011 Generalized Farm
18 28433 * 2 ^ 7830457 + 1 2357207 SB7 2004
19 3 * 2 ^ 7033641 + 1 2117338 L2233 2011 Splits OF (7033639.3)
20 33661 * 2 ^ 7031232 + 1 2116617 SB11 2007
21 2 ^ 6972593-1 2098960 G4 1999 Mersenn 38
22 6679881 * 2 ^ 6679881 + 1 2010852 Cullen 2009952
23 1582137 * 2 ^ 6328550 + 1 1905090 L801 Cullen 2009
24 3 * 2 ^ 6090515-1 1833429 L1353 2010
25 7 * 2 ^ 5775996 + 1 1738749 L3325 2012
26 252191 * 2 ^ 5497878-1 1655032 L3183 2012
27 258317 * 2 ^ 5450519 + 1 1640776 g414 2008
28 773620 ^ 262144 + 1 1543643 L3118 2012 Generalized Farm
29 3 * 2 ^ 5082306 + 1 1529928 L780 2009
Shares OF (5082303,3), OF (5082305,5)
30 676754 ^ 262144 + 1 1528413 L2975 2012 Generalized Farm
31 5359 * 2 ^ 5054502 + 1 1521561 SB6 2003
32 525094 ^ 262144 + 1 1499526 p338 2012 Generalized Farm
33 265711 * 2 ^ 4858008 + 1 1462412 g414 2008
34 1271 * 2 ^ 4850526-1 1460157 L1828 2012
35 361658 ^ 262144 + 1 1457075 p332 2011 Generalized Farm
36 9 * 2 ^ 4683555-1 1409892 L1828 2012
37 121 * 2 ^ 4553899-1 1370863 L3023 2012
38 145310 ^ 262144 + 1 1353265 p314 2011 Generalized Farm
39 353159 * 2 ^ 4331116-1 1303802 L2408 2011
40 141941 * 2 ^ 4299438-1 1294265 L689 2011
41 3 * 2 ^ 4235414-1 1274988 L606 2008
42 191 * 2 ^ 4203426-1 1265360 L2484 2012
43 40734 ^ 262144 + 1 1208473 p309 2011 Generalized Farm
44 9 * 2 ^ 4005979-1 1205921 L1828 2012
45 27 * 2 ^ 3855094-1 1160501 L3033 2012
46 24518 ^ 262144 + 1 1150678 g413 2008 Generalized Farm
47 123547 * 2 ^ 3804809-1 1145367 L2371 2011
48 415267 * 2 ^ 3771929-1 1135470 L2373 2011
49 938237 * 2 ^ 3752950-1 1129757 L521 2007 Wudala
50 65531 * 2 ^ 3629342-1 1092546 L2269 2011
51 485767 * 2 ^ 3609357-1 1086531 L622 2008
52 5 * 2 ^ 3569154-1 1074424 L503 2009
53 1019 * 2 ^ 3536312-1 1064539 L1828 2012
54 7 * 2 ^ 3511774 + 1 1057151 p236 2008 Splits OF (3511773.6)
55 428639 * 2 ^ 3506452-1 1055553 L2046 2011
56 9 * 2 ^ 3497442 + 1 1052836 L1780 2012 Generalized Farm
57 1273 * 2 ^ 3448551-1 1038121 L1828 2012
58 191249 * 2 ^ 3417696-1 1028835 L1949 2010
59 59 * 2 ^ 3408416-1 1026038 L426 2010
60 81 * 2 ^ 3352924 + 1 1009333 L1728 2012 Generalized Farm
61 1087 * 2 ^ 3336385-1 1004355 L1828 2012
62 3139 * 2 ^ 3321905-1 999997 L185 2008
63 4847 * 2 ^ 3321063 + 1 999744 SB9 2005
64 223 * 2 ^ 3264459-1 982703 L1884 2012
65 9 * 2 ^ 3259381-1 981173 L1828 2011
66 113983 * 2 ^ 3201175-1 963655 L613 2008
67 1087 * 2 ^ 3164677-1 952666 L1828 2012
68 15 * 2 ^ 3162659 + 1 952057 p286 2012
69 19 * 2 ^ 3155009-1 949754 L1828 2012
70 3 * 2 ^ 3136255-1 944108 L256 2007
71 1019 * 2 ^ 3103680-1 934304 L1828 2012
72 5 * 2 ^ 3090860-1 930443 L1862 2012
73 21 * 2 ^ 3065701 + 1 922870 p286 2012
74 5 * 2 ^ 3059698-1 921062 L503 2008
75 383731 * 2 ^ 3021377-1 909531 L466 2011
76 2 ^ 3021377-1 909526 G3 1998 Mersenn 37
77 7 * 2 ^ 3015762 + 1 907836 g279 2008
78 1095 * 2 ^ 2992587-1 900862 L1828 2011
79 15 * 2 ^ 2988834 + 1 899730 p286 2012
80 4348099 * 2 ^ 2976221-1 895939 L466 2008
81 2 ^ 2976221-1 895932 G2 1997 Mersenn 36
82 198677 * 2 ^ 2950515 + 1 888199 L2121 2012
83 7 * 2 ^ 2915954 + 1 877791 g279 2008 Splits OF (2915953,12)
84 427194 * 113 ^ 427194 + 1 877069 p310 2012 Generalized Cullen
85 1207 * 2 ^ 2861901-1 861522 L1828 2011
86 222361 * 2 ^ 2854840 + 1 859398 g403 2006
87 177 * 2 ^ 2816050 + 1 847718 L129 2012
88 96 * 10 ^ 846519-1 846521 L2425 2011 Almost repdigit
89 15 * 2 ^ 2785940 + 1 838653 p286 2012
90 17 * 2 ^ 2721830-1 819354 p294 2010
91 165 * 2 ^ 2717378-1 818015 L2055 2012
92 45 * 2 ^ 2711732 + 1 816315 L1349 2012
93 1372930 ^ 131072 + 1 804474 g236 2003 Generalized Farm
94 1361244 ^ 131072 + 1 803988 g236 2004 Generalized Farm
95 1176694 ^ 131072 + 1 795695 g236 2003 Generalized Farm
96 13 * 2 ^ 2642943-1 795607 L1862 2012
97 342673 * 2 ^ 2639439-1 794556 L53 2007
98 1243 * 2 ^ 2623707-1 789818 L1828 2011
99 13 * 2 ^ 2606075-1 784508 L1862 2011
100 334310 * 211 ^ 334310-1 777037 p350 2012 Generalized Woods Cataldi, Descartes, Fermat, Mersenne, Leibniz, Euler, and many other mathematicians fought over the search for the largest possible prime numbers. In the course of solving this riddle, many sections of number theory were developed (for example, Fermat's small theorem and the quadratic law of reciprocity). In the 20th century, this search led to the creation of new fast ways to multiply integers: in 1968, mathematician Folker Strassen figured out how to use the fast Fourier transform for this. Now this method is known as the Strassen algorithm, its improved version is used in the GIMPS software and everywhere for the rapid multiplication of matrices.
The mystery of Mersenne's primes and the search for new primes have instilled a love for mathematics in many schoolchildren, who as a result chose a scientific and engineering career for themselves.
In general, the search for new prime numbers, and especially Mersenne numbers, can be compared to collecting rare things.
Source: https://habr.com/ru/post/168417/
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