# 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 January 2016, 164 (probable) megaprimes are known, including 150 definitely primes[2] and 14 probable primes.[3] 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.[4][5]

The term bevaprime has been proposed as a term for a prime with at least 1,000,000,000 digits.[5]

In fact, "almost all" primes are megaprimes, as the amount of primes with more than a million digits is infinite. However, the vast majority of known primes are not megaprimes.

## 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
274207281 – 1 2016-01-07 22,338,618 Prime
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 2006-09-04 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
${\displaystyle {\tfrac {2^{13372531}+1}{3}}}$ 2013-09 4,025,533 PRP
${\displaystyle {\tfrac {2^{13347311}+1}{3}}}$ 2013-09 4,017,941 PRP
19249×213018586 + 1 2007-03-26 3,918,990 Prime
3×211895718 − 1 2015-06 3,580,969 Prime
3×211731850 − 1 2015-03-13 3,531,640 Prime
3×211484018 − 1 2014-11-22 3,457,035 Prime
3×210829346 + 1 2014-01-14 3,259,959 Prime
475856524288 + 1 2012-08-08 2,976,633 Prime
356926524288 + 1 2012-06-20 2,911,151 Prime
341112524288 + 1 2012-06-15 2,900,832 Prime
27653×29167433 + 1 2005 2,759,677 Prime
90527 × 29162167 + 1 2010 2,758,093 Prime
29092392 + 40291 2011-02 2,737,083 PRP
2038×3661028507 − 1 2016 2,636,562 Prime
75898524288 + 1 2011-11-19 2,558,647 Prime
28433×27830457 + 1 2004 2,357,207 Prime
502573×27181987 − 1 2014-10-04 2,162,000 Prime
402539×27173024 − 1 2014-10-02 2,159,301 Prime
161041×27107964 + 1 2015-01 2,139,716 Prime
3×27033641 + 1 2011-02-21 2,117,338 Prime
33661×27031232 + 1 2007 2,116,617 Prime
26972593 – 1 1999-06-01 2,098,960 Prime
40597×26808509 – 1 2013-12-25 2,049,571 Prime
6679881×26679881 + 1 2009-07-25 2,010,852 Prime
37×26660841 − 1 2014 2,005,115 Prime
304207×26643565 – 1 2013-10-10 1,999,918 Prime
398023×26418059 – 1 2013-10-05 1,932,034 Prime
6328548×26328548 + 1 2009-04-20 1,905,090 Prime
3×26090515 – 1 2010-04-24 1,833,429 Prime
1583×25989282 − 1 2015 1,802,957 Prime
7×25775996 + 1 2012-11-02 1,738,749 Prime
9×25642513 + 1 2013 1,698,567 Prime
2622×111621920 – 1 2015 1,689,060 Prime
252191×25497878 – 1 2012-06-23 1,655,032 Prime
258317 × 25450519+1 2008 1,640,776 Prime
1615588262144 + 1 2016 1,627,477 Prime
1488256262144 + 1 2016 1,618,131 Prime
1415198262144 + 1 2016 1,612,400 Prime
27×25213635 + 1 2015 1,569,462 Prime
25146295 + 41693 2009-11 1,549,190 PRP
773620262144 + 1 2012-04-19 1,543,643 Prime
51×25085142 - 1 2014 1,530,782 Prime
3×25082306 + 1 2009-04-03 1,529,928 Prime
676754262144+1 2012 1,528,413 Prime
296024 × 52185270 − 1 2016 1,527,444 Prime
5359 × 25054502+1 2003 1,521,561 Prime
13×24998362 + 1 2014 1,504,659 Prime
525094262144+1 2012 1,499,526 Prime
92158×52145024 + 1 2016 1,499,313 Prime
77072×52139921 + 1 2016 1,495,746 Prime
306398 × 52112410 − 1 2016 1,476,517 Prime
265711 × 24858008+1 2008 1,462,412 Prime
154222 × 52091432 + 1 2015 1,461,854 Prime
1271 × 24850526-1 2012 1,460,157 Prime
362978262144 − 362978131072 + 1 2015 1,457,490 Prime
361658262144+1 2011 1,457,075 Prime
100186 × 52079747 − 1 2015 1,453,686 Prime
653 × 101435026 − 1 2014 1,435,029 Prime
144052× 52018290 + 1 2015 1,410,730 Prime
9 × 24683555 − 1 2012 1,409,892 Prime
11 × 24643238 − 1 2014 1,397,755 Prime
192098262144 − 192098131072 + 1 2015 1,385,044 Prime
27 × 24583717 − 1 2014 1,379,838 Prime
24583176 + 2131 2009-09 1,379,674 PRP
121×24553899 – 1 2012-02-25 1,370,863 Prime
27× 24542344 − 1 2014 1,367,384 Prime
${\displaystyle {\tfrac {2^{4533073}+2^{2266537}+1}{5}}}$ 2014-03 1,364,591 PRP
145310262144+1 2011 1,353,265 Prime
36772 × 61723287 − 1 2014 1,340,983 Prime
${\displaystyle {\tfrac {13^{1199467}+1}{14}}}$ 2015-12 1,336,138 PRP
353159×24331116 – 1 2011-05-31 1,303,802 Prime
141941×24299438 – 1 2011-05-26 1,294,265 Prime
15 × 24246384+1 2013 1,278,291 Prime
3×24235414 – 1 2008-03-23 1,274,988 Prime
109208 × 51816285 + 1 2014 1,269,534 Prime
191 × 24203426-1 2012 1,265,360 Prime
${\displaystyle {\tfrac {2^{4187251}-1}{72234342371519}}}$ 2016-05 1,260,475 PRP
${\displaystyle {\tfrac {14^{1091401}+1}{15}}}$ 2014-03 1,250,885 PRP
${\displaystyle {\tfrac {16^{1025393}+1}{17}}}$ 2014-08 1,234,695 PRP
${\displaystyle {\tfrac {2^{4031399}+1}{3}}}$ 2010-02 1,213,572 PRP
40734262144+1 2011 1,208,473 Prime
9 × 24005979 - 1 2012 1,205,921 Prime
12 × 68656921 + 1 2016 1,203,815 Prime
1993191 × 41993191 − 1 2015 1,200,027 Prime
27×23855094 – 1 2012-02-28 1,160,501 Prime
24518262144+1 2008 1,150,678 Prime
123547×23804809 – 1 2011-05-08 1,145,367 Prime
415267×23771929 – 1 2011-05-08 1,135,470 Prime
11 × 23771821+1 2013 1,135,433 Prime
938237 × 23752950-1 2007 1,129,757 Prime
23451 × 23739388 + 1 2015 1,125,673 Prime
23704053 + 21852027 + 1 2014 1,115,032 Prime
330286×51584399 – 1 2014-03-21 1,107,453 Prime
15×23668194 – 1 2013 1,104,238 Prime
65531 × 23629342-1 2011 1,092,546 Prime
${\displaystyle {\tfrac {106\cdot 23^{800873}-7}{11}}}$ 2015-05 1,090,573 PRP
485767 × 23609357-1 2008 1,086,531 Prime
5 × 23569154-1 2009 1,074,424 Prime
81 × 492399095 − 1 1,074,352 Prime
22934×51536762 – 1 2014-02-06 1,074,155 Prime
${\displaystyle {\tfrac {7^{1264699}-1}{6}}}$ 2014-01 1,068,794 PRP
178658×51525224 – 1 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 2012-10-23 1,052,836 Prime
51×23490971 + 1 2014 1,050,889 Prime
59912×51500861 + 1 2014-01-17 1,049,062 Prime
${\displaystyle {\tfrac {2^{3464473}-1}{604874508299177}}}$ 2014-10 1,042,896 PRP
37292×51487989 + 1 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
24 × 414391179 + 1 1,023,717 Prime
67×23391385 – 1 2014 1,020,911 Prime
173198×51457792 – 1 2013-12-04 1,018,959 Prime
81×23352924 + 1 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 2013 1,000,000 Prime
10999999 + 593499 2012-12-24 1,000,000 PRP

## References

1. ^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
2. Chris Caldwell, The Largest Known Primes at The Prime Pages.
3. Henri Lifchitz & Renaud Lifchitz, Probable Primes Top 10000, primenumbers.net
4. ^ GIMPS press release, GIMPS Finds First Million-Digit Prime. Retrieved on 2008-01-04.
5. ^ a b Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
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12. Generalized Sierpinski/Riesel primes
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42. ^ Patrick De Geest, 10^999999 + y, World!Of Numbers