Megaprime

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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 December 2018, 449 (probable) megaprimes are known, including 421 definite primes[2] and 28 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.[6]

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

Known megaprimes and mega PRPs[edit]

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

Rank (only for proven primes)[7] Number Discovery date Decimal digits Prime / PRP
1 282589933 – 1 2018-12-07 24,862,048 Prime
2 277232917 – 1 2017-12-26 23,249,425 Prime
3 274207281 – 1 2016-01-07 22,338,618 Prime
4 257885161 – 1 2013-01-25 17,425,170 Prime
5 243112609 – 1 2008-08-23 12,978,189 Prime
6 242643801 – 1 2009-06-04 12,837,064 Prime
7 237156667 – 1 2008-09-06 11,185,272 Prime
8 232582657 – 1 2006-09-04 9,808,358 Prime
9 10223×231172165 + 1 2016-11 9,383,761 Prime
10 230402457 – 1 2005-12-15 9,152,052 Prime
11 225964951 – 1 2005-02-18 7,816,230 Prime
12 224036583 – 1 2004-05-15 7,235,733 Prime
13 220996011 – 1 2003-11-17 6,320,430 Prime
14 10590941048576 + 1 2018 6,317,602 Prime
15 9194441048576 + 1 2017-09-02 6,253,210 Prime
16 168451×219375200 + 1 2017 5,832,522 Prime
17 2017 5,338,805 Prime
18 8508301*217016603-1 2018 5,122,515 Prime
19 2017 4,055,114 Prime
20 213466917 – 1 2001-11-14 4,053,946 Prime
- 2013-09 4,025,533 PRP
- 2013-09 4,017,941 PRP
21 19249×213018586 + 1 2007-03-26 3,918,990 Prime
22 3×211895718 − 1 2015-06 3,580,969 Prime
23 3×211731850 − 1 2015-03-13 3,531,640 Prime
24 3×211484018 − 1 2014-11-22 3,457,035 Prime
25 193997*211452891 +1 2018 3,447,670 Prime
26 2312092524288+1 2018 3,336,572 Prime
27 2061748524288+1 L4783 2018 3,310,478 Prime
28 1880370524288 + 1 2018 3,289,511 Prime
29 3×210829346 + 1 2014-01-14 3,259,959 Prime
30 2017 3,107,335 Prime
31 2017 3,068,389 Prime
32 475856524288 + 1 2012-08-08 2,976,633 Prime
33 1806676*411806676+1 2018 2,913,785 Prime
34 356926524288 + 1 2012-06-20 2,911,151 Prime
35 341112524288 + 1 2012-06-15 2,900,832 Prime
36 27653×29167433 + 1 2005 2,759,677 Prime
37 90527×29162167 + 1 2010 2,758,093 Prime
- 29092392 + 40291 2011-02 2,737,083 PRP
38 1323365*1161323365+1 2018 2,732,038 Prime
39 273809×28932416 − 1 2017 2,688,931 Prime
40 2038×3661028507 − 1 2016 2,636,562 Prime
41 75898524288 + 1 2011-11-19 2,558,647 Prime
42 28433×27830457 + 1 2004 2,357,207 Prime
43 1341174×531341174 + 1 2017 2,312,561 Prime
44 2017 2,259,865 Prime
- 2018 2,201,714 PRP
45 737×27269322 − 1 2017 2,188,287 Prime
46 502573×27181987 − 1 2014-10-04 2,162,000 Prime
47 402539×27173024 − 1 2014-10-02 2,159,301 Prime
48 3343×27166019 - 1 2016 2,157,191 Prime
49 161041×27107964 + 1 2015-01 2,139,716 Prime
- 2017-10 2,131,318 PRP
50 27*27046834+1 2018 2,121,310 Prime
51 3×27033641 + 1 2011-02-21 2,117,338 Prime
52 33661×27031232 + 1 2007 2,116,617 Prime
53 2017 2,114,016 Prime
54 26972593 – 1 1999-06-01 2,098,960 Prime
55 4×721119849 − 1 2016 2,079,933 Prime
56 127*26836153-1 2018 2,057,890 Prime
57 40597×26808509 – 1 2013-12-25 2,049,571 Prime
58 6679881×26679881 + 1 2009-07-25 2,010,852 Prime
59 37×26660841 − 1 2014 2,005,115 Prime
60 304207×26643565 – 1 2013-10-10 1,999,918 Prime
61 398023×26418059 – 1 2013-10-05 1,932,034 Prime
62 1582137x26328550 + 1 2009-04-20 1,905,090 Prime
63 194368*52638045-1 2018 1,843,920 Prime
64 66916*5^2628609-1 2018 1,837,324 Prime
65 3×26090515 – 1 2010-04-24 1,833,429 Prime
66 1583×25989282 − 1 2015 1,802,957 Prime
67 327926*52542838-1 2018 1,777,374 Prime
68 81556*52539960+1 2018 1,775,361 Prime
69 5828034262144+1 2018 1,773,542 Prime
70 5205422262144+1 2018 1,760,679 Prime
71 5152128262144+1 2018 1,759,508 Prime
72 4489246262144+1 2018 1,743,828 Prime
73 7×25775996 + 1 2012-11-02 1,738,749 Prime
74 4246258262144+1 2018 1,737,493 Prime
75 3933508262144+1 2018 1,728,783 Prime
76 3853792262144+1 2018 1,726,452 Prime
77 3673932262144 + 1 2017 1,721,010 Prime
78 3596074262144 + 1 2017 1,718,572 Prime
79 3547726262144 + 1 2017 1,717,031 Prime
80 1243×25686715 - 1 2016 1,711,875 Prime
81 3060772262144 + 1 2017 1,700,222 Prime
82 9×25642513 + 1 2013 1,698,567 Prime
83 2622×111621920 – 1 2015 1,689,060 Prime
84 2676404262144 + 1 2017 1,684,945 Prime
86 301562×52408646 - 1 2017 1,683,577 Prime
86 2611294262144 + 1 2017 1,682,141 Prime
87 171362×52400996 − 1 2017 1,678,230 Prime
88 2514168262144 + 1 2017 1,677,825 Prime
89 252191×25497878 – 1 2012-06-23 1,655,032 Prime
90 2042774262144 + 1 2016 1,654,187 Prime
91 1828858262144+1 2016 1,641,593 Prime
92 258317 × 25450519+1 2008 1,640,776 Prime
93 5*2^5429494-1 2017 1,634,442 Prime
94 43*2^5408183-1 2018 1,628,027 Prime
94 1615588262144 + 1 2016 1,627,477 Prime
95 1349×25385004 − 1 2017 1,621,051 Prime
96 1488256262144 + 1 2016 1,618,131 Prime
97 1415198262144 + 1 2016 1,612,400 Prime
98 2017 1,581,846 Prime
- 2016-07 1,577,600 PRP
99 180062×52249192 − 1 2016 1,572,123 Prime
100 27×25213635 + 1 2015 1,569,462 Prime
101 2017 1,553,498 Prime
102 53546×52216664-1 2016 1,549,387 Prime
- 25146295 + 41693 2009-11 1,549,190 PRP
103 773620262144 + 1 2012-04-19 1,543,643 Prime
104 51×25085142 - 1 2014 1,530,782 Prime
105 3×25082306 + 1 2009-04-03 1,529,928 Prime
106 676754262144+1 2012 1,528,413 Prime
107 296024 × 52185270 − 1 2016 1,527,444 Prime
108 5359 × 25054502+1 2003 1,521,561 Prime
109 13×24998362 + 1 2014 1,504,659 Prime
110 525094262144+1 2012 1,499,526 Prime
111 92158×52145024 + 1 2016 1,499,313 Prime
112 77072×52139921 + 1 2016 1,495,746 Prime
113 306398 × 52112410 − 1 2016 1,476,517 Prime
114 265711 × 24858008+1 2008 1,462,412 Prime
115 154222 × 52091432 + 1 2015 1,461,854 Prime
116 1271 × 24850526-1 2012 1,460,157 Prime
117 2015 1,457,490 Prime
118 361658262144+1 2011 1,457,075 Prime
- 2017-01 1,455,425 PRP
119 100186 × 52079747 − 1 2015 1,453,686 Prime
120 [*] 2014 1,442,553 Prime
121 653 × 101435026 − 1 2014 1,435,029 Prime
122 1229 x 24703492-1 2018 1,415,896
123 144052× 52018290 + 1 2015 1,410,730 Prime
124 9 × 24683555 − 1 2012 1,409,892 Prime
125 34x993469245+1 2018 1,406,305 Prime
126 79x24658115-1 2018 1,402,235 Prime
127 11 × 24643238 − 1 2014 1,397,755 Prime
128 68×995465908 − 1 2017 1,396,712 Prime
129 2015 1,385,044 Prime
130 27 × 24583717 − 1 2014 1,379,838 Prime
- 24583176 + 2131 2009-09 1,379,674 PRP
131 121×24553899 – 1 2012-02-25 1,370,863 Prime
132 27× 24542344 − 1 2014 1,367,384 Prime
- [*] 2014-03 1,364,591 PRP
133 4×797468702 + 1 2017 1,359,920 Prime
134 145310262144+1 2011 1,353,265 Prime
135 36772 × 61723287 − 1 2014 1,340,983 Prime
- 2015-12 1,336,138 PRP
136 151×24424321 − 1 2016 1,331,856 Prime
- 2018 1,319,850 PRP
137 49x24365175-1 2017 1,314,051 Prime
138 49x24360869-1 2017 1,312,755 Prime
139 13x24333087-1 2018 1,304,391 Prime
140 353159×24331116 – 1 2011-05-31 1,303,802 Prime
141 682156×79682156 + 1 2016 1,294,484 Prime
142 141941×24299438 – 1 2011-05-26 1,294,265 Prime
143 15 × 24246384+1 2013 1,278,291 Prime
144 3×24235414 – 1 2008-03-23 1,274,988 Prime
145 109208 × 51816285 + 1 2014 1,269,534 Prime
146 1091x24215518-1 2018 1,269,001
147 191 × 24203426-1 2012 1,265,360 Prime
148 1259 × 24196028-1 2016 1,263,134 Prime
- 2017-07 1,262,611 PRP
149 325918x51803339-1 2014 1,260,486 Prime
- 2016-05 1,260,475 PRP
- 2014-03 1,250,885 PRP
150 133778x51785689+1 2014 1,248,149 Prime
151 17x24107544-1 2015 1,236,496 Prime
152 24032x51768249+1 2014 1,235,958 Prime
153 172×159561319 − 1 2017 1,235,689 Prime
- 2014-08 1,234,695 PRP
154 1031×24054974−1 2017 1,220,672 Prime
- 2010-02 1,213,572 PRP
155 39653×430460397-1 2016 1,212,446 Prime
156 40734262144+1 2011 1,208,473 Prime
157 9 × 24005979 - 1 2012 1,205,921 Prime
158 12 × 68656921 + 1 2016 1,203,815 Prime
159 67×688423893 + 1 2017 1,202,836 Prime
160 1993191 × 41993191 − 1 2015 1,200,027 Prime
161 138172x51714207-1 2014 1,198,185 Prime
162 Phi(3,-1202113^98304) 2016 1,195,366 Prime
163 Phi(3,-1110815^98304) 2016 1,188,622 Prime
164 22478x51675150-1 2014 1,170,884 Prime
165 1199x23889576-1 2018 1,170,883 Prime
166 298989x23886857+1 2014 1,170,067 Prime
167 27×23855094 – 1 2012-02-28 1,160,501 Prime
168 164x978387920-1 2018 1,160,015 Prime
169 30x514424652-1 2017 1,151,218 Prime
170 24518262144+1 2008 1,150,678 Prime
171 Phi(3,-700219^98304) 2016 1,149,220 Prime
172 109x980383669-1 2018 1,147,643 Prime
173 123547×23804809 – 1 2011-05-08 1,145,367 Prime
174 2564x75610753+1 2014 1,145,203 Prime
175 Phi(3,-660955^98304) 2016 1,144,293 Prime
176 326834x51634978-1 2014 1,142,807 Prime
177 415267×23771929 – 1 2011-05-08 1,135,470 Prime
178 11 × 23771821+1 2013 1,135,433 Prime
179 938237 × 23752950-1 2007 1,129,757 Prime
180 207394x51612573-1 2014 1,127,146 Prime
181 684×101127118 + 1 2017 1,127,121 Prime
182 Phi(3,-535386^98304) 2016 1,126,302 Prime
183 104944x51610735-1 2014 1,125,861 Prime
184 23451 × 23739388 + 1 2015 1,125,673 Prime
185 23704053 + 21852027 + 1 2014 1,115,032 Prime
186 330286×51584399 – 1 2014-03-21 1,107,453 Prime
187 13x23675223-1 2016 1,106,354 Prime
188 15×23668194 – 1 2013 1,104,238 Prime
189 13*23664703-1 2016 1,103,187 Prime
190 Phi(3,-406515^98304) 2016 1,102,790 Prime
191 33300×430417849-1 2016 1,100,397 Prime
192 65531 × 23629342-1 2011 1,092,546 Prime
193 113x23628034-1 2014 1,092,150 Prime
- 2015-05 1,090,573 PRP
194 29x920367810-1 2015 1,090,113 Prime
195 14641x2^3618876+1 2018 1,089,395 Prime
196 485767 × 23609357-1 2008 1,086,531 Prime
197 189x23596375+1 2016 1,082,620 Prime
198 35x23587843+1 2014 1,080,050 Prime
199 275x23585539+1 2016 1,079,358 Prime
200 2x59608685+1 2014 1,077,892 Prime
201 309x23577339+1 2016 1,076,889 Prime
202 251x23574535+1 2016 1,076,045 Prime
203 35x23570777+1 2014 1,074,913 Prime
204 33x23570132+1 2014 1,074,719 Prime
205 5 × 23569154-1 2009 1,074,424 Prime
206 81 × 492399095 − 1 2015 1,074,352 Prime
207 22934×51536762 – 1 2014-02-06 1,074,155 Prime
208 771x23564109+1 2018 1,072,907 Prime
209 381x23563676+1 2016 1,072,776 Prime
210 555x23563328+1 2018 1,072,672 Prime
211 1183x23560584+1 2018 1,071,846 Prime
212 415x23559614+1 2016 1,071,554 Prime
213 1103x23558176-1 2018 1,071,121 Prime
214 1379x23557072-1 2018 1,070,789 Prime
215 681x23553141+1 2018 1,069,605 Prime
216 599x23551793+1 2018 1,069,200 Prime
217 621x23551472+1 2018 1,069,103 Prime
- 2014-01 1,068,794 PRP
218 773x23550373+1 2018 1,068,772 Prime
219 1199x23548380-1 2018 1,068,172 Prime
220 191x23548117+1 2015 1,068,092 Prime
221 867x23547711+1 2018 1,067,971 Prime
222 Phi(3,3^1118781+1)/3 2014 1,067,588 Prime
223 351x23545752+1 2016 1,067,381 Prime
224 93x23544744+1 2014 1,067,077 Prime
225 1159x23543702+1 2018 1,066,764 Prime
226 178658x51525224 – 1 2014-01-31 1,066,092 Prime
227 1085x23539671+1 2018 1,065,551 Prime
228 465×23536871 – 1 2016-09-30 1,064,707 Prime
229 1019 × 23536312-1 2012 1,064,539 Prime
230 1179x23534450+1 2018 1,063,979 Prime
231 447x23533656+1 2016 1,063,740 Prime
232 1059x23533550+1 2016 1,063,529 Prime
234 553x23532758+1 2018 1,063,469 Prime
235 141x23529287+1 2015 1,062,424 Prime
236 13x23527315-1 2016 1,061,829 Prime
237 1393x23525571-1 2017 1,061,306 Prime
238 1071x23523944+1 2018 1,060,816 Prime
239 329x23518451+1 2016 1,059,162 Prime
240 135x23518338+1 2015 1,059,128 Prime
241 2×101059002 – 1 2013 1,059,003 Prime
242 64x101058794+1 2017 1,058,796 Prime
243 599x23515959+1 2018 1,058,412 Prime
244 7 × 23511774+1 2008 1,057,151 Prime
245 1135x23510890+1 2018 1,056,887 Prime
246 428639 × 23506452-1 2011 1,055,553 Prime
247 555x23502765+1 2018 1,054,441 Prime
248 643x23501974+1 2018 1,054,203 Prime
249 2x23774109+1 2014 1,054,127 Prime
250 1159x23501490+1 2018 1,054,057 Prime
253 9×23497442 + 1 2012-10-23 1,052,836 Prime
256 51×23490971 + 1 2014 1,050,889 Prime
261 59912×51500861 + 1 2014-01-17 1,049,062 Prime
- 2014-10 1,042,896 PRP
274 37292×51487989 + 1 2013-12-29 1,040,065 Prime
275 1273 × 23448551-1 2012 1,038,121 Prime
293 191249 × 23417696-1 2010 1,028,835 Prime
298 59 × 23408416-1 2010 1,026,038 Prime
302 24 × 414391179 + 1 2016 1,023,717 Prime
307 342924651×23394939 – 1 2017 1,021,988 Prime
312 67×23391385 – 1 2014 1,020,911 Prime
315 173198×51457792 – 1 2013-12-04 1,018,959 Prime
356 81×23352924 + 1 2012-01-17 1,009,333 Prime
384 1087 × 23336385-1 2012 1,004,355 Prime
410 464253×23321908 – 1 2013 1,000,000 Prime
412 191273×23321908 – 1 2013 1,000,000 Prime
- 10999999 + 593499 2012-12-24 1,000,000 PRP

All numbers from 10999999 through 10999999 + 593498 are known to be composite, and there is a very high probability 10999999 + 593499, a strong PRP, is actually the smallest megaprime.[48]

The last prime that is not a megaprime is almost certainly 10999999 - 172473.[3]

Notes[edit]

^ * = gcd(,the aurifeuillean L part of ), = gcd(,the aurifeuillean M part of ).

See also[edit]

References[edit]

  1. ^ Chris Caldwell, The Prime Glossary: megaprime at The Prime Pages. Retrieved on 2008-01-04.
  2. ^ a b c d e f g Chris Caldwell, The Largest Known Primes at The Prime Pages.
  3. ^ a b c d e f g h i j k l m n o p q r s t u v 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. ^ Chris Caldwell, The Largest Known Prime by Year: A Brief History at The Prime Pages. Retrieved on 2008-09-28.
  6. ^ Chris Caldwell, The Largest Known Prime by Year: A Brief History at the Wayback Machine (archived 2016 January 1)
  7. ^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
  8. ^ Entry for the number
  9. ^ Entry for the number
  10. ^ Entry for the number, http://primes.utm.edu
  11. ^ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
  12. ^ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
  13. ^ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
  14. ^ Official announcement of discovery of 475856524288 + 1, PrimeGrid
  15. ^ Official announcement of discovery of 356926524288 + 1, PrimeGrid
  16. ^ Official announcement of discovery of 341112524288 + 1, PrimeGrid
  17. ^ a b c d e f g h i j k l m n o p q Generalized Sierpinski/Riesel primes
  18. ^ Official announcement of discovery of 75898524288 + 1, PrimeGrid
  19. ^ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  20. ^ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  21. ^ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  22. ^ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
  23. ^ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid
  24. ^ Official announcement of discovery of 304207×26643565 – 1, PrimeGrid
  25. ^ Official announcement of discovery of 398023×26418059 – 1, PrimeGrid
  26. ^ Official announcement of discovery of 6328548×26328548 + 1, PrimeGrid
  27. ^ Official announcement of discovery of 3×26090515 – 1, PrimeGrid
  28. ^ Official announcement of discovery of 7×25775996 + 1, PrimeGrid
  29. ^ Official announcement of discovery of 252191×25497878 – 1, PrimeGrid
  30. ^ Official announcement of discovery of 773620262144 + 1, PrimeGrid
  31. ^ Official announcement of discovery of 3×25082306 + 1, PrimeGrid
  32. ^ Official announcement of discovery of 121×24553899 – 1, PrimeGrid
  33. ^ Official announcement of discovery of 353159×24331116 – 1, PrimeGrid
  34. ^ Official announcement of discovery of 141941×24299438 – 1, PrimeGrid
  35. ^ Official announcement of discovery of 3×24235414 – 1, PrimeGrid
  36. ^ Official announcement of discovery of 27×23855094 – 1, PrimeGrid
  37. ^ Official announcement of discovery of 123547×23804809 – 1, PrimeGrid
  38. ^ Official announcement of discovery of 415267×23771929 – 1, PrimeGrid
  39. ^ Official announcement of discovery of 330286×51584399 – 1, PrimeGrid
  40. ^ Official announcement of discovery of 22934×51536762 – 1, PrimeGrid
  41. ^ Official announcement of discovery of 178658×51525224 – 1, PrimeGrid
  42. ^ Official announcement of discovery of 465×23536871 – 1, PrimeGrid
  43. ^ Official announcement of discovery of 9×23497442 + 1, PrimeGrid
  44. ^ Official announcement of discovery of 59912×51500861 + 1, PrimeGrid
  45. ^ Official announcement of discovery of 37292×51487989 + 1, PrimeGrid
  46. ^ Official announcement of discovery of 173198×51457792 – 1, PrimeGrid
  47. ^ Official announcement of discovery of 81×23352924 + 1, PrimeGrid
  48. ^ a b Patrick De Geest, 10^999999 + y, World!Of Numbers

External links[edit]