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Megaprime

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Megaprime

A megaprime is a prime number with at least one million decimal digits[1] (whereas titanic prime is a prime number with at least 1,000 digits, and gigantic prime has at least 10,000 digits).

The number of megaprimes found by year.

As of 21 October 2014, 114 megaprimes are known.[2] The first to be found was the Mersenne prime 26972593−1 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the distributed computing project GIMPS.[3][4]

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.[4]

Contents

  • Known megaprimes and mega PRPs 1
  • See also 2
  • References 3
  • External links 4

Known megaprimes and mega PRPs

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not. See the article Probable prime.

Number Discovery date Decimal digits Prime / PRP
257885161 – 1 2013-01-25 17,425,170 Prime
243112609 – 1 2008-08-23 12,978,189 Prime
242643801 – 1 2009-04-12 12,837,064 Prime
237156667 – 1 2008-09-06 11,185,272 Prime
232582657 – 1 2006 9,808,358 Prime
230402457 – 1 2005-12-15 9,152,052 Prime
225964951 – 1 2005-02-18 7,816,230 Prime
224036583 – 1 2004-05-15 7,235,733 Prime
220996011 – 1 2003-11-17 6,320,430 Prime
213466917 – 1 2001-11-14 4,053,946 Prime
\tfrac{2^{13372531}+1}{3}
[5]
2013-09 4,025,533 PRP
\tfrac{2^{13347311}+1}{3}
[5]
2013-09 4,017,941 PRP
19249×213018586 + 1
[2]
2007-03-26 3,918,990 Prime
3×210829346 + 1
[6]
2014-01-14 3,259,959 Prime
475856524288 + 1
[7]
2012-08-08 2,976,633 Prime
356926524288 + 1
[8]
2012-06-20 2,911,151 Prime
341112524288 + 1
[9]
2012-06-15 2,900,832 Prime
27653×29167433 + 1
[2]
2005 2,759,677 Prime
90527 × 29162167 + 1 2010 2,758,093 Prime
29092392 + 40291
[5]
2011-02 2,737,083 PRP
75898524288 + 1
[10]
2011-11-19 2,558,647 Prime
28433×27830457 + 1
[2]
2004 2,357,207 Prime
3×27033641 + 1
[11]
2011-02-21 2,117,338 Prime
33661×27031232 + 1
[2]
2007 2,116,617 Prime
26972593 – 1 1999-06-01 2,098,960 Prime
40597×26808509 – 1
[12]
2013-12-25 2,049,571 Prime
6679881×26679881 + 1
[13]
2009-07-25 2,010,852 Prime
304207×26643565 – 1
[14]
2013-10-10 1,999,918 Prime
398023×26418059 – 1
[15]
2013-10-05 1,932,034 Prime
6328548×26328548 + 1
[16]
2009-04-20 1,905,090 Prime
3×26090515 – 1
[17]
2010-04-24 1,833,429 Prime
7×25775996 + 1
[18]
2012-11-02 1,738,749 Prime
9×25642513 + 1 2013 1,698,567 Prime
252191×25497878 – 1
[19]
2012-06-23 1,655,032 Prime
258317 × 25450519+1 2008 1,640,776 Prime
25146295 + 41693
[5]
2009-11 1,549,190 PRP
773620262144 + 1
[20]
2012-04-19 1,543,643 Prime
3×25082306 + 1
[21]
2009-04-03 1,529,928 Prime
676754262144+1 2012 1,528,413 Prime
5359 × 25054502+1 2003 1,521,561 Prime
525094262144+1 2012 1,499,526 Prime
265711 × 24858008+1 2008 1,462,412 Prime
1271 × 24850526-1 2012 1,460,157 Prime
361658262144+1 2011 1,457,075 Prime
9 × 24683555-1 2012 1,409,892 Prime
24583176 + 2131
[5]
2009-09 1,379,674 PRP
121×24553899 – 1
[22]
2012-02-25 1,370,863 Prime
145310262144+1 2011 1,353,265 Prime
353159×24331116 – 1
[23]
2011-05-31 1,303,802 Prime
141941×24299438 – 1
[24]
2011-05-26 1,294,265 Prime
15 × 24246384+1 2013 1,278,291 Prime
3×24235414 – 1
[25]
2008-03-23 1,274,988 Prime
191 × 24203426-1 2012 1,265,360 Prime
\tfrac{14^{1091401}+1}{15}
[5]
2014-03 1,250,885 PRP
\tfrac{2^{4031399}+1}{3}
[5]
2010-02 1,213,572 PRP
40734262144+1 2011 1,208,473 Prime
9 × 24005979-1 2012 1,205,921 Prime
27×23855094 – 1
[26]
2012-02-28 1,160,501 Prime
24518262144+1 2008 1,150,678 Prime
123547×23804809 – 1
[27]
2011-05-08 1,145,367 Prime
415267×23771929 – 1
[28]
2011-05-08 1,135,470 Prime
11 × 23771821+1 2013 1,135,433 Prime
938237 × 23752950-1 2007 1,129,757 Prime
330286×51584399 – 1
[29]
2014-03-21 1,107,453 Prime
15×23668194 – 1 2013 1,104,238 Prime
65531 × 23629342-1 2011 1,092,546 Prime
485767 × 23609357-1 2008 1,086,531 Prime
5 × 23569154-1 2009 1,074,424 Prime
22934×51536762 – 1
[30]
2014-02-06 1,074,155 Prime
\tfrac{7^{1264699}-1}{6}
[5]
2014-01 1,068,794 PRP
178658×51525224 – 1
[31]
2014-01-31 1,066,092 Prime
1019 × 23536312-1 2012 1,064,539 Prime
2×101059002 – 1 2013 1,059,003 Prime
7 × 23511774+1 2008 1,057,151 Prime
428639 × 23506452-1 2011 1,055,553 Prime
9×23497442 + 1
[32]
2012-10-23 1,052,836 Prime
51×23490971 + 1 2014 1,050,889 Prime
59912×51500861 + 1
[33]
2014-01-17 1,049,062 Prime
37292×51487989 + 1
[34]
2013-12-29 1,040,065 Prime
1273 × 23448551-1 2012 1,038,121 Prime
191249 × 23417696-1 2010 1,028,835 Prime
59 × 23408416-1 2010 1,026,038 Prime
67×23391385 – 1 2014 1,020,911 Prime
173198×51457792 – 1
[35]
2013-12-04 1,018,959 Prime
81×23352924 + 1
[36]
2012-01-17 1,009,333 Prime
1087 × 23336385-1 2012 1,004,355 Prime
464253×23321908 – 1 2013 1,000,000 Prime
191273×23321908 – 1
[2]
2013 1,000,000 Prime
10999999 + 593499
[37]
2012-12-24 1,000,000 PRP

See also

References

  1. ^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
  2. ^ a b c d e f Chris Caldwell, The Largest Known Primes at The Prime Pages. Retrieved on 2014-10-21.
  3. ^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
  4. ^ a b Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
  5. ^ a b c d e f g h Probable Primes Top 10000, primenumbers.net
  6. ^ + 110829346Official announcement of discovery of 3×2, PrimeGrid
  7. ^ + 1524288Official announcement of discovery of 475856, PrimeGrid
  8. ^ + 1524288Official announcement of discovery of 356926, PrimeGrid
  9. ^ + 1524288Official announcement of discovery of 341112, PrimeGrid
  10. ^ + 1524288Official announcement of discovery of 75898, PrimeGrid
  11. ^ + 17033641Official announcement of discovery of 3×2, PrimeGrid
  12. ^ – 16808509Official announcement of discovery of 40597×2, PrimeGrid
  13. ^ + 16679881Official announcement of discovery of 6679881×2, PrimeGrid
  14. ^ – 16643565Official announcement of discovery of 304207×2, PrimeGrid
  15. ^ – 16418059Official announcement of discovery of 398023×2, PrimeGrid
  16. ^ + 16328548Official announcement of discovery of 6328548×2, PrimeGrid
  17. ^ – 16090515Official announcement of discovery of 3×2, PrimeGrid
  18. ^ + 15775996Official announcement of discovery of 7×2, PrimeGrid
  19. ^ – 15497878Official announcement of discovery of 252191×2, PrimeGrid
  20. ^ + 1262144Official announcement of discovery of 773620, PrimeGrid
  21. ^ + 15082306Official announcement of discovery of 3×2, PrimeGrid
  22. ^ – 14553899Official announcement of discovery of 121×2, PrimeGrid
  23. ^ – 14331116Official announcement of discovery of 353159×2, PrimeGrid
  24. ^ – 14299438Official announcement of discovery of 141941×2, PrimeGrid
  25. ^ – 14235414Official announcement of discovery of 3×2, PrimeGrid
  26. ^ – 13855094Official announcement of discovery of 27×2, PrimeGrid
  27. ^ – 13804809Official announcement of discovery of 123547×2, PrimeGrid
  28. ^ – 13771929Official announcement of discovery of 415267×2, PrimeGrid
  29. ^ – 11584399Official announcement of discovery of 330286×5, PrimeGrid
  30. ^ – 11536762Official announcement of discovery of 22934×5, PrimeGrid
  31. ^ – 11525224Official announcement of discovery of 178658×5, PrimeGrid
  32. ^ + 13497442Official announcement of discovery of 9×2, PrimeGrid
  33. ^ + 11500861Official announcement of discovery of 59912×5, PrimeGrid
  34. ^ + 11487989Official announcement of discovery of 37292×5, PrimeGrid
  35. ^ – 11457792Official announcement of discovery of 173198×5, PrimeGrid
  36. ^ + 13352924Official announcement of discovery of 81×2, PrimeGrid
  37. ^ Patrick De Geest, 10^999999 + y, World!Of Numbers

External links

  • Chris Caldwell, The Largest Known Primes Database at The Prime Pages.
  • PrimeGrid’s 321 Prime Search, about the discovery of 3×26090515−1.
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