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Known megaprimes and mega PRPs

[edit]
complete 1~250

Entries labelled "Prime" have been proved prime; those labelled "PRP" have not. See the article Probable prime. There are currently 412 proven mega primes.[1]

Rank (only for proven primes)[2] Number Discovery date Decimal digits Prime / PRP
1 277232917 – 1 2017-12-26 23,249,425 Prime
2 274207281 – 1 2016-01-07 22,338,618 Prime
3 257885161 – 1 2013-01-25 17,425,170 Prime
4 243112609 – 1 2008-08-23 12,978,189 Prime
5 242643801 – 1 2009-04-12 12,837,064 Prime
6 237156667 – 1 2008-09-06 11,185,272 Prime
7 232582657 – 1 2006-09-04 9,808,358 Prime
8 10223×231172165 + 1 2016-11 9,383,761 Prime
9 230402457 – 1 2005-12-15 9,152,052 Prime
10 225964951 – 1 2005-02-18 7,816,230 Prime
11 224036583 – 1 2004-05-15 7,235,733 Prime
12 220996011 – 1 2003-11-17 6,320,430 Prime
13 10590941048576 + 1 2018 6,317,602 Prime
14 9194441048576 + 1 2017-09-02 6,253,210 Prime
15 168451×219375200 + 1 2017 5,832,522 Prime
16 2017 5,338,805 Prime
17 8508301*217016603-1 2018 5,122,515
18 2017 4,055,114 Prime
19 213466917 – 1 2001-11-14 4,053,946 Prime
- 2013-09 4,025,533 PRP
- 2013-09 4,017,941 PRP
20 19249×213018586 + 1 2007-03-26 3,918,990 Prime
21 3×211895718 − 1 2015-06 3,580,969 Prime
22 3×211731850 − 1 2015-03-13 3,531,640 Prime
23 3×211484018 − 1 2014-11-22 3,457,035 Prime
24 193997*211452891 +1 2018 3,447,670 Prime
25 2312092524288+1 2018 3,336,572 Prime
26 2061748524288+1 L4783 2018 3,310,478 Prime
27 1880370524288 + 1 2018 3,289,511 Prime
28 3×210829346 + 1 2014-01-14 3,259,959 Prime
29 2017 3,107,335 Prime
30 2017 3,068,389 Prime
31 475856524288 + 1 2012-08-08 2,976,633 Prime
32 1806676*411806676+1 2018 2,913,785 Prime
33 356926524288 + 1 2012-06-20 2,911,151 Prime
34 341112524288 + 1 2012-06-15 2,900,832 Prime
35 27653×29167433 + 1 2005 2,759,677 Prime
36 90527×29162167 + 1 2010 2,758,093 Prime
- 29092392 + 40291 2011-02 2,737,083 PRP
37 1323365*1161323365+1 2018 2,732,038 Prime
38 273809×28932416 − 1 2017 2,688,931 Prime
39 2038×3661028507 − 1 2016 2,636,562 Prime
40 75898524288 + 1 2011-11-19 2,558,647 Prime
41 28433×27830457 + 1 2004 2,357,207 Prime
42 1341174×531341174 + 1 2017 2,312,561 Prime
43 2017 2,259,865 Prime
- 2018 2,201,714 PRP
44 737×27269322 − 1 2017 2,188,287 Prime
45 502573×27181987 − 1 2014-10-04 2,162,000 Prime
46 402539×27173024 − 1 2014-10-02 2,159,301 Prime
47 3343×27166019 - 1 2016 2,157,191 Prime
48 161041×27107964 + 1 2015-01 2,139,716 Prime
- 2017-10 2,131,318 PRP
49 27*27046834+1 2018 2,121,310 Prime
50 3×27033641 + 1 2011-02-21 2,117,338 Prime
51 33661×27031232 + 1 2007 2,116,617 Prime
52 2017 2,114,016 Prime
53 26972593 – 1 1999-06-01 2,098,960 Prime
54 4×721119849 − 1 2016 2,079,933 Prime
55 127*26836153-1 2018 2,057,890 Prime
56 40597×26808509 – 1 2013-12-25 2,049,571 Prime
57 6679881×26679881 + 1 2009-07-25 2,010,852 Prime
58 37×26660841 − 1 2014 2,005,115 Prime
59 304207×26643565 – 1 2013-10-10 1,999,918 Prime
60 398023×26418059 – 1 2013-10-05 1,932,034 Prime
61 1582137x26328550 + 1 2009-04-20 1,905,090 Prime
62 194368*52638045-1 2018 1,843,920 Prime
63 66916*5^2628609-1 2018 1,837,324 Prime
64 3×26090515 – 1 2010-04-24 1,833,429 Prime
65 1583×25989282 − 1 2015 1,802,957 Prime
66 327926*52542838-1 2018 1,777,374 Prime
67 81556*52539960+1 2018 1,775,361 Prime
68 5828034262144+1 2018 1,773,542 Prime
69 5205422262144+1 2018 1,760,679 Prime
70 5152128262144+1 2018 1,759,508 Prime
71 4489246262144+1 2018 1,743,828 Prime
72 7×25775996 + 1 2012-11-02 1,738,749 Prime
73 4246258262144+1 2018 1,737,493 Prime
74 3933508262144+1 2018 1,728,783 Prime
75 3853792262144+1 2018 1,726,452 Prime
76 3673932262144 + 1 2017 1,721,010 Prime
77 3596074262144 + 1 2017 1,718,572 Prime
78 3547726262144 + 1 2017 1,717,031 Prime
79 1243×25686715 - 1 2016 1,711,875 Prime
80 3060772262144 + 1 2017 1,700,222 Prime
81 9×25642513 + 1 2013 1,698,567 Prime
82 2622×111621920 – 1 2015 1,689,060 Prime
83 2676404262144 + 1 2017 1,684,945 Prime
84 301562×52408646 - 1 2017 1,683,577 Prime
85 2611294262144 + 1 2017 1,682,141 Prime
86 171362×52400996 − 1 2017 1,678,230 Prime
87 2514168262144 + 1 2017 1,677,825 Prime
88 252191×25497878 – 1 2012-06-23 1,655,032 Prime
89 2042774262144 + 1 2016 1,654,187 Prime
90 1828858262144+1 2016 1,641,593 Prime
91 258317 × 25450519+1 2008 1,640,776 Prime
92 5*2^5429494-1 2017 1,634,442 Prime
93 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 1,145,203 2014 Prime
175 Phi(3,-660955^98304) 1,144,293 2016 Prime
176 326834x51634978-1 1,142,807 2014 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 1103187 Prime
190 Phi(3,-406515^98304) 2016 1102790 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 1056887 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.[44]

  1. ^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
  2. ^ Caldwell, Chris K. "THE LARGEST KNOWN PRIMES (The 5,000 largest known primes)". Retrieved 23 November 2018.
  3. ^ Entry for the number
  4. ^ Entry for the number, http://primes.utm.edu
  5. ^ a b c d e f g h i j k l m n o p q r s t Cite error: The named reference PRPTop was invoked but never defined (see the help page).
  6. ^ a b c d e f Cite error: The named reference The_largest_known_primes was invoked but never defined (see the help page).
  7. ^ Official announcement of discovery of 3×211731850 − 1, PrimeGrid
  8. ^ Official announcement of discovery of 3×211484018 − 1, PrimeGrid
  9. ^ Official announcement of discovery of 3×210829346 + 1, PrimeGrid
  10. ^ Official announcement of discovery of 475856524288 + 1, PrimeGrid
  11. ^ Official announcement of discovery of 356926524288 + 1, PrimeGrid
  12. ^ Official announcement of discovery of 341112524288 + 1, PrimeGrid
  13. ^ a b c d e f g h i j k l m n o p q Generalized Sierpinski/Riesel primes
  14. ^ Official announcement of discovery of 75898524288 + 1, PrimeGrid
  15. ^ Official announcement of discovery of 502573×27181987 − 1, PrimeGrid
  16. ^ Official announcement of discovery of 402539×27173024 − 1, PrimeGrid
  17. ^ Official announcement of discovery of 3×27033641 + 1, PrimeGrid
  18. ^ Official announcement of discovery of 40597×26808509 – 1, PrimeGrid
  19. ^ Official announcement of discovery of 6679881×26679881 + 1, PrimeGrid
  20. ^ Official announcement of discovery of 304207×26643565 – 1, PrimeGrid
  21. ^ Official announcement of discovery of 398023×26418059 – 1, PrimeGrid
  22. ^ Official announcement of discovery of 6328548×26328548 + 1, PrimeGrid
  23. ^ Official announcement of discovery of 3×26090515 – 1, PrimeGrid
  24. ^ Official announcement of discovery of 7×25775996 + 1, PrimeGrid
  25. ^ Official announcement of discovery of 252191×25497878 – 1, PrimeGrid
  26. ^ Official announcement of discovery of 773620262144 + 1, PrimeGrid
  27. ^ Official announcement of discovery of 3×25082306 + 1, PrimeGrid
  28. ^ Official announcement of discovery of 121×24553899 – 1, PrimeGrid
  29. ^ Official announcement of discovery of 353159×24331116 – 1, PrimeGrid
  30. ^ Official announcement of discovery of 141941×24299438 – 1, PrimeGrid
  31. ^ Official announcement of discovery of 3×24235414 – 1, PrimeGrid
  32. ^ Official announcement of discovery of 27×23855094 – 1, PrimeGrid
  33. ^ Official announcement of discovery of 123547×23804809 – 1, PrimeGrid
  34. ^ Official announcement of discovery of 415267×23771929 – 1, PrimeGrid
  35. ^ Official announcement of discovery of 330286×51584399 – 1, PrimeGrid
  36. ^ Official announcement of discovery of 22934×51536762 – 1, PrimeGrid
  37. ^ Official announcement of discovery of 178658×51525224 – 1, PrimeGrid
  38. ^ Official announcement of discovery of 465×23536871 – 1, PrimeGrid
  39. ^ Official announcement of discovery of 9×23497442 + 1, PrimeGrid
  40. ^ Official announcement of discovery of 59912×51500861 + 1, PrimeGrid
  41. ^ Official announcement of discovery of 37292×51487989 + 1, PrimeGrid
  42. ^ Official announcement of discovery of 173198×51457792 – 1, PrimeGrid
  43. ^ Official announcement of discovery of 81×23352924 + 1, PrimeGrid
  44. ^ a b Patrick De Geest, 10^999999 + y, World!Of Numbers