What is a PRP ?
A PRP is a probable prime number, a number that nobody knows how to prove
or disprove its primality.
Here are some criterions that can be used to recognize theses numbers
:
- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N
should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3.
N should pass the strong test in base b.
- or more (if someone has got an idea) !!!
Submit your PRPs
See the Top discoverers
See the Latest PRPs
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| Rank |
Probable prime |
Digits (> 10000) |
Who ? |
When ? |
| 1 | 2^9092392+40291 | 2737083 | Engracio Esmenda / Five or Bust | 02/2011 |
| 2 | 2^5146295+41693 | 1549190 | Engracio Esmenda / Five or Bust | 11/2009 |
| 3 | 2^4583176+2131 | 1379674 | Ben Maloney / Five or Bust | 09/2009 |
| 4 | (2^4031399+1)/3 | 1213572 | Tony Reix / Diepeveen-Underwood -Reix | 02/2010 |
| 5 | 10^999999+593499 | 1000000 | Peter Kaiser | 02/2013 |
| 6 | 2^2249255+28433 | 677094 | Ben Maloney / Five or Bust | 01/2009 |
| 7 | (18^481147+1)/19 | 603970 | Paul Bourdelais | 07/2011 |
| 8 | (2^1882787-2^941394+1)/5 | 566775 | Borys Jaworski | 11/2012 |
| 9 | 8^615997-7^615997 | 556301 | Jean-Louis Charton | 07/2009 |
| 10 | 3^1059503-2^1059503 | 505512 | Mike Oakes | 04/2012 |
| 11 | (2^1669219-2^834610+1)/5 | 502485 | Borys Jaworski | 01/2011 |
| 12 | (6^608099-1)/5 | 473193 | Paul Bourdelais | 05/2010 |
| 13 | 2^1518191+75353 | 457022 | Ben Maloney / Five or Bust | 01/2009 |
| 14 | (10^424861-7)/3 | 424861 | Leonid Durman | 01/2012 |
| 15 | 138^196873-137^196873 | 421285 | Jean-Louis Charton | 12/2009 |
| 16 | (3^877843-1)/2 | 418838 | Paul Bourdelais | 07/2010 |
| 17 | F(1968721) | 411439 | Henri Lifchitz | 11/2009 |
| 18 | (2^1347781-2^673891+1)/5 | 405722 | Borys Jaworski | 10/2008 |
| 19 | (10^380976-7)/3 | 380976 | Leonid Durman | 01/2012 |
| 20 | F(1803059) | 376817 | Henri Lifchitz | 06/2009 |
| 21 | 2^1191375+8543 | 358640 | Phil Moore | 06/2008 |
| 22 | (2^1168183-1)/54763676838381762583 | 351639 | Matthias Wurtinger | 01/2011 |
| 23 | (2^1148729+2^574365+1)/5 | 345802 | Borys Jaworski | 03/2007 |
| 24 | F(1636007) | 341905 | Henri Lifchitz | 03/2009 |
| 25 | (2^1127239+2^563620+1)/5 | 339333 | Borys Jaworski | 11/2006 |
| 26 | (3^700897+1)/4 | 334413 | Paul Bourdelais | 04/2010 |
| 27 | (7^371669-1)/6 | 314096 | Paul Bourdelais | 02/2010 |
| 28 | (11^293831-1)/10 | 305993 | Paul Bourdelais | 03/2010 |
| 29 | 8^336419-7^336419 | 303817 | Jean-Louis Charton | 01/2008 |
| 30 | 10^300476+3 | 300477 | Ed Trice | 10/2012 |
| 31 | 314738^9+9^314738 | 300337 | Anatoly F. Selevich | 02/2011 |
| 32 | 7^355039-6^355039 | 300043 | Jean-Louis Charton | 05/2011 |
| 33 | (2^986191+1)/3 | 296873 | Vincent Diepeveen | 06/2008 |
| 34 | 2^983620+60451 | 296100 | Phil Moore | 03/2008 |
| 35 | (11*2^948635-13)/15 | 285568 | Renaud Lifchitz | 11/2011 |
| 36 | 10^282493-9^282493 | 282493 | Jean-Louis Charton | 03/2007 |
| 37 | 3^591827-2^591827 | 282374 | Mike Oakes | 08/2009 |
| 38 | 757^96487-756^96487 | 277796 | Jean-Louis Charton | 12/2012 |
| 39 | (5^396413-1)/4 | 277081 | Paul Bourdelais | 06/2010 |
| 40 | (7*10^271757-61)/9 | 271757 | Erik Branger | 03/2012 |
| 41 | (10^270343-1)/9 | 270343 | Maksym Voznyy | 07/2007 |
| 42 | F(1285607) | 268676 | Henri Lifchitz | 11/2008 |
| 43 | (10^268207+1)/11 | 268206 | Paul Bourdelais | 02/2010 |
| 44 | (19^209359-1)/18 | 267718 | Paul Bourdelais | 08/2010 |
| 45 | (7*10^260198-61)/9 | 260198 | Erik Branger | 11/2011 |
| 46 | (11*2^857159-13)/15 | 258031 | Renaud Lifchitz | 08/2011 |
| 47 | 11^246668-90 | 256879 | Enzo Doria | 12/2012 |
| 48 | 11^246167-90 | 256357 | Enzo Doria | 12/2012 |
| 49 | 11^243796-90 | 253888 | Enzo Doria | 12/2012 |
| 50 | 11^242579-60 | 252620 | Enzo Doria | 10/2012 |
| 51 | 846^83761-845^83761 | 245200 | Jean-Louis Charton | 12/2012 |
| 52 | 11^227092-90 | 236492 | Enzo Doria | 11/2012 |
| 53 | (5^335429+1)/6 | 234455 | Paul Bourdelais | 08/2010 |
| 54 | (11^223999+1)/12 | 233270 | Paul Bourdelais | 02/2010 |
| 55 | 10^232599-3 | 232599 | Markus Tervooren | 10/2010 |
| 56 | 3^485977-2^485977 | 231870 | Mike Oakes | 09/2009 |
| 57 | (3^483611-1)/2 | 230741 | Paul Bourdelais | 02/2010 |
| 58 | (18^180181-1)/17 | 226176 | Andy Steward | 04/2007 |
| 59 | 2^750740-3 | 225996 | Paul Bourdelais | 03/2012 |
| 60 | 234178^9+9^234178 | 223463 | Anatoly F. Selevich | 07/2011 |
| 61 | 11^213654-180 | 222498 | Enzo Doria | 01/2013 |
| 62 | 10^221631-9 | 221631 | Alexander Gramolin | 02/2011 |
| 63 | L(1051849) | 219824 | Renaud Lifchitz | 03/2009 |
| 64 | 11^210961-240 | 219694 | Enzo Doria | 01/2013 |
| 65 | F(1049897) | 219416 | Henri Lifchitz | 10/2008 |
| 66 | 277^88301-276^88301 | 215674 | Jean-Louis Charton | 06/2012 |
| 67 | 11^206081-10^206081 | 214612 | Jean-Louis Charton | 10/2011 |
| 68 | 227^89797+2 | 211565 | Lelio R Paula | 08/2012 |
| 69 | 2^702194-3 | 211382 | Paul Bourdelais | 03/2012 |
| 70 | 11^202357-1140 | 210734 | Enzo Doria | 12/2012 |
| 71 | (5^300893+4^300893)/9 | 210315 | Jean-Louis Charton | 11/2011 |
| 72 | (21^156217-1)/20 | 206552 | Paul Bourdelais | 04/2010 |
| 73 | 2^685578+3 | 206380 | Paul Bourdelais | 04/2012 |
| 74 | 326^81943-325^81943 | 205941 | Jean-Louis Charton | 07/2012 |
| 75 | (2^684127-1)/23765203727 | 205933 | Jens K. Andersen | 04/2009 |
| 76 | 4^341233-3^341233 | 205443 | Jean-Louis Charton | 01/2006 |
| 77 | 2^678561+678561 | 204268 | Henri Lifchitz | 05/2006 |
| 78 | 5^289937-4^289937 | 202658 | Jean-Louis Charton | 03/2013 |
| 79 | 6^258413-5^258413 | 201085 | Jean-Louis Charton | 03/2013 |
| 80 | (53*10^198529+1)/9 | 198530 | Serge Batalov | 07/2010 |
| 81 | (18^157051-1)/17 | 197141 | Paul Bourdelais | 03/2010 |
| 82 | (44*10^196684+1)/9 | 196685 | Serge Batalov | 07/2010 |
| 83 | 11^187185-90 | 194934 | Enzo Doria | 09/2012 |
| 84 | 15^165559-14^165559 | 194713 | Jean-Louis Charton | 03/2011 |
| 85 | F(931517) | 194676 | Henri Lifchitz | 09/2008 |
| 86 | (5^277183+1)/6 | 193742 | Paul Bourdelais | 07/2010 |
| 87 | (35*10^191073+1)/9 | 191074 | Serge Batalov | 07/2010 |
| 88 | L(901657) | 188436 | Renaud Lifchitz | 11/2008 |
| 89 | 11^179143-4170 | 186559 | Enzo Doria | 12/2012 |
| 90 | (5^266863+1)/6 | 186529 | Paul Bourdelais | 07/2010 |
| 91 | (3^388897+2^388897)/5 | 185551 | Jean-Louis Charton | 09/2011 |
| 92 | 5^265007-4^265007 | 185232 | Jean-Louis Charton | 02/2013 |
| 93 | (9^193247+1)/10 | 184404 | Paul Bourdelais | 02/2010 |
| 94 | 11^176176-240 | 183469 | Enzo Doria | 11/2012 |
| 95 | (20^140053+1)/21 | 182212 | Paul Bourdelais | 04/2010 |
| 96 | 11^174145-360 | 181354 | Enzo Doria | 10/2012 |
| 97 | Gamma-Prime(179849) | 179849 | Eric W. Weisstein | 06/2011 |
| 98 | (2^148330+1)^4-2 | 178608 | Cletus Emmanuel | 12/2003 |
| 99 | (18^142031-1)/17 | 178287 | Paul Bourdelais | 03/2010 |
| 100 | ReverseConsecutiveIntegerPrime(37765) | 177719 | Eric W. Weisstein | 04/2010 |
| 101 | 10^175608+2971 | 175609 | Mike Oakes | 05/2010 |
| 102 | 5^246497-4^246497 | 172295 | Jean-Louis Charton | 11/2008 |
| 103 | 11^164009-270 | 170798 | Enzo Doria | 10/2012 |
| 104 | 2^566496+7 | 170533 | Donovan Johnson | 07/2006 |
| 105 | (7^201653+1)/8 | 170416 | Paul Bourdelais | 02/2010 |
| 106 | 393^64747-392^64747 | 167980 | Jean-Louis Charton | 08/2012 |
| 107 | 589^60089-588^60089 | 166454 | Jean-Louis Charton | 09/2012 |
| 108 | 11^159756-2424 | 166369 | Mike Oakes | 06/2010 |
| 109 | 2^551542+19249 | 166031 | Payam Samidoost | 08/2002 |
| 110 | 11^158160-60 | 164707 | Enzo Doria | 07/2012 |
| 111 | 919^54919-918^54919 | 162743 | Jean-Louis Charton | 01/2013 |
| 112 | 9^170099-8^170099 | 162316 | Jean-Louis Charton | 05/2005 |
| 113 | 2^538104+1531 | 161986 | Lelio R Paula | 01/2013 |
| 114 | 3^336353-2^336353 | 160482 | Mike Oakes | 10/2007 |
| 115 | 11^152420-210 | 158730 | Enzo Doria | 09/2012 |
| 116 | 2^525690-9221 | 158249 | Lelio R Paula | 01/2013 |
| 117 | 8^173687-7^173687 | 156855 | Jean-Louis Charton | 09/2004 |
| 118 | 53^90679-52^90679 | 156356 | Robert Price | 01/2013 |
| 119 | 2^517698+4429 | 155843 | Lelio R Paula | 01/2013 |
| 120 | EPrime(155025) | 155025 | Eric W. Weisstein | 10/2010 |
| 121 | (6^196337+1)/7 | 152780 | Paul Bourdelais | 02/2010 |
| 122 | 578^55117-577^55117 | 152230 | Jean-Louis Charton | 08/2012 |
| 123 | 2^505431-505431 | 152150 | Henri Lifchitz | 04/2005 |
| 124 | 2^504054-2231 | 151736 | Yves Minet | 10/2011 |
| 125 | 2^502576-4019 | 151291 | Yves Minet | 10/2011 |
| 126 | (12^139739+1)/13 | 150803 | Paul Bourdelais | 09/2011 |
| 127 | (31^101111-1)/30 | 150792 | Alexander Zhirkov | 11/2010 |
| 128 | 2^500899-500899 | 150786 | Henri Lifchitz | 04/2005 |
| 129 | 2^499534-221 | 150375 | Yves Minet | 06/2012 |
| 130 | 413^56963-412^56963 | 149013 | Jean-Louis Charton | 08/2012 |
| 131 | 47^89113-46^89113 | 149006 | Robert Price | 10/2012 |
| 132 | 8*10^148860-3 | 148861 | Ray Chandler | 04/2011 |
| 133 | (8*10^148328+1)/9 | 148328 | Serge Batalov | 05/2010 |
| 134 | 2^491391-7807 | 147924 | Lelio R Paula | 01/2013 |
| 135 | 2^483302-3221 | 145489 | Lelio R Paula | 12/2012 |
| 136 | 53^84239-52^84239 | 145252 | Robert Price | 01/2013 |
| 137 | 2^481801-481801 | 145037 | Henri Lifchitz | 03/2005 |
| 138 | 29^99167+2 | 145022 | Ray Chandler | 08/2011 |
| 139 | (8*10^144683+1)/9 | 144683 | Serge Batalov | 05/2010 |
| 140 | L(692147) | 144651 | Henri Lifchitz | 10/2008 |
| 141 | 2^479844+3 | 144448 | Donovan Johnson | 06/2006 |
| 142 | (11*2^475553-7)/15 | 143156 | Renaud Lifchitz | 03/2011 |
| 143 | 2^474053+2897 | 142705 | Lelio R Paula | 08/2012 |
| 144 | 898^48311-897^48311 | 142676 | Jean-Louis Charton | 12/2012 |
| 145 | 2^470173-16465 | 141537 | Enzo Doria | 04/2013 |
| 146 | 143^(2^16)+106^(2^16) | 141253 | Valeryi Kuryshev | 02/2011 |
| 147 | (5^201359-1)/4 | 140744 | Paul Bourdelais | 12/2008 |
| 148 | floor(Pi*10^140344)%10^140165 | 140165 | Serge Batalov | 08/2012 |
| 149 | (17^113621+1)/18 | 139804 | Paul Bourdelais | 09/2011 |
| 150 | (26*10^139289+1)/9 | 139290 | Serge Batalov | 05/2010 |
| 151 | 2^459768+1531 | 138404 | Lelio R Paula | 06/2012 |
| 152 | 555555*2^458524+1513 | 138036 | Darren Bedwell | 08/2009 |
| 153 | 2^458465+2^32+1 | 138012 | T. D. Noe | 06/2007 |
| 154 | 2^457822+105 | 137819 | Donovan Johnson | 06/2006 |
| 155 | 11^132315-360 | 137792 | Enzo Doria | 09/2012 |
| 156 | (71*10^137250+1)/9 | 137251 | Serge Batalov | 05/2010 |
| 157 | 124^(2^16)+57^(2^16) | 137195 | Valeryi Kuryshev | 02/2011 |
| 158 | (37^87421-1)/36 | 137093 | Robert Price | 03/2012 |
| 159 | 2^454675-1777 | 136871 | Yves Minet | 10/2011 |
| 160 | L(651821) | 136223 | Henri Lifchitz | 09/2008 |
| 161 | (13725^32768+1)/131074 | 135573 | Lelio R Paula | 03/2012 |
| 162 | (5^193939+1)/6 | 135557 | Paul Bourdelais | 12/2008 |
| 163 | 2^446494-16485 | 134409 | Enzo Doria | 04/2013 |
| 164 | (89*10^133580+1)/9 | 133581 | Serge Batalov | 05/2010 |
| 165 | 62^74521-61^74521 | 133571 | Robert Price | 05/2013 |
| 166 | L(637751) | 133283 | Henri Lifchitz | 09/2008 |
| 167 | 2^441063+383 | 132774 | Lelio R Paula | 06/2012 |
| 168 | 47^79201-46^79201 | 132432 | Robert Price | 10/2012 |
| 169 | L(631181) | 131910 | Henri Lifchitz | 09/2008 |
| 170 | 35^85243-34^85243 | 131621 | Robert Price | 05/2012 |
| 171 | (2^435808+1)/641/6700417 | 131182 | Lelio R Paula | 02/2012 |
| 172 | (11*2^428881-7)/15 | 129106 | Renaud Lifchitz | 03/2011 |
| 173 | L(616787) | 128901 | Henri Lifchitz | 09/2008 |
| 174 | 11^123594-240 | 128710 | Enzo Doria | 09/2012 |
| 175 | 11^122629-720 | 127705 | Enzo Doria | 11/2012 |
| 176 | 11^121910-840 | 126957 | Enzo Doria | 12/2012 |
| 177 | 331^50339-10004 | 126846 | Enzo Doria | 07/2012 |
| 178 | F(604711) | 126377 | Henri Lifchitz | 02/2005 |
| 179 | 2^419637+29 | 126324 | Henri Lifchitz | 02/2006 |
| 180 | 2^418829+167 | 126081 | Lelio R Paula | 01/2012 |
| 181 | (23^91943-1)/22 | 125201 | Robert Price | 01/2012 |
| 182 | 43125^27010-106 | 125185 | Enzo Doria | 08/2012 |
| 183 | 2^415144-3683 | 124971 | Yves Minet | 10/2011 |
| 184 | 2^414032-5 | 124637 | Henri Lifchitz | 07/2006 |
| 185 | 2^412868-120599 | 124286 | Paul Bourdelais | 02/2012 |
| 186 | F(593689) | 124074 | Henri Lifchitz | 01/2005 |
| 187 | (5^177337+1)/6 | 123953 | Paul Bourdelais | 11/2008 |
| 188 | F(590041) | 123311 | Henri Lifchitz | 01/2005 |
| 189 | 11^117642-300 | 122512 | Enzo Doria | 10/2012 |
| 190 | (30^82883-1)/29 | 122427 | Robert Price | 12/2011 |
| 191 | (2^406583-1)/813167 | 122388 | Jens K. Andersen | 02/2009 |
| 192 | 3^256199-2^256199 | 122238 | Mike Oakes | 06/2005 |
| 193 | 2^404501-631 | 121767 | Yves Minet | 07/2012 |
| 194 | (17*10^121621+1)/9 | 121622 | Serge Batalov | 05/2010 |
| 195 | 11^116555-720 | 121380 | Enzo Doria | 11/2012 |
| 196 | (17*10^121242+1)/9 | 121243 | Serge Batalov | 05/2010 |
| 197 | 2^400424-216413 | 120540 | Enzo Doria | 04/2013 |
| 198 | 2^399918-95 | 120388 | Lelio R Paula | 04/2013 |
| 199 | 2^398877+105 | 120074 | Donovan Johnson | 01/2006 |
| 200 | 2^398710+57 | 120024 | Lelio R Paula | 04/2013 |
| 201 | L(574219) | 120005 | Renaud Lifchitz | 03/2004 |
| 202 | 2^398571+60413 | 119982 | Yves Minet | 03/2011 |
| 203 | 8*10^119930-3 | 119931 | Ray Chandler | 04/2011 |
| 204 | 11^114738-150 | 119488 | Enzo Doria | 10/2012 |
| 205 | 2^396790-21 | 119446 | Lelio R Paula | 04/2013 |
| 206 | 2^394034-3 | 118617 | M. Frind & P. Underwood | 09/2002 |
| 207 | 2^393180+73 | 118359 | Lelio R Paula | 04/2013 |
| 208 | (53*10^118216+1)/9 | 118217 | Serge Batalov | 11/2010 |
| 209 | (7*2^392697+1)/15 | 118214 | Renaud Lifchitz | 03/2011 |
| 210 | 2^391933+5897 | 117984 | Yves Minet | 02/2011 |
| 211 | 2^391324+90901 | 117801 | Yves Minet | 02/2011 |
| 212 | 2^390779-30337 | 117637 | Paul Bourdelais | 02/2012 |
| 213 | 11^112916-780 | 117590 | Enzo Doria | 12/2012 |
| 214 | 31^78759-30 | 117459 | Theodore Burton | 02/2007 |
| 215 | 2^389998+37 | 117402 | Lelio R Paula | 03/2013 |
| 216 | 2^389478+43 | 117245 | Lelio R Paula | 03/2013 |
| 217 | 2^388888-1529 | 117067 | Yves Minet | 01/2013 |
| 218 | 2^388469-43 | 116941 | Lelio R Paula | 03/2013 |
| 219 | 2^388180+93 | 116854 | Donovan Johnson | 07/2008 |
| 220 | (30^78857-1)/29 | 116480 | Robert Price | 12/2011 |
| 221 | 2^385969-823 | 116189 | Yves Minet | 05/2012 |
| 222 | 2^385564+781 | 116067 | Lelio R Paula | 01/2012 |
| 223 | 2^384953-111943 | 115883 | Paul Bourdelais | 02/2012 |
| 224 | 2^384834+93 | 115847 | Donovan Johnson | 07/2008 |
| 225 | (71*10^115810-17)/9 | 115811 | Ray Chandler | 08/2011 |
| 226 | 2^384312+81091 | 115690 | Yves Minet | 02/2010 |
| 227 | (11*2^383859-13)/15 | 115553 | Renaud Lifchitz | 03/2011 |
| 228 | 2^383560-455 | 115464 | Yves Minet | 03/2012 |
| 229 | (12^106859+1)/13 | 115320 | Paul Bourdelais | 02/2010 |
| 230 | 2^382198+9 | 115054 | Lelio R Paula | 03/2013 |
| 231 | 2^381806-4481 | 114936 | Yves Minet | 07/2011 |
| 232 | 569^41651-568^41651 | 114754 | Jean-Louis Charton | 11/2009 |
| 233 | 2^380700+91 | 114603 | Lelio R Paula | 03/2013 |
| 234 | 10^114575+3^114576 | 114576 | Mike Oakes | 09/2010 |
| 235 | 2*10^113941+9 | 113942 | Dmitry Domanov | 11/2010 |
| 236 | 2^378272-16565 | 113872 | Enzo Doria | 04/2013 |
| 237 | 2^378198+67 | 113849 | Lelio R Paula | 03/2013 |
| 238 | 6^146274-18893 | 113824 | Enzo Doria | 03/2013 |
| 239 | 2^378078+75 | 113813 | Lelio R Paula | 03/2013 |
| 240 | 2^377940+63 | 113772 | Lelio R Paula | 03/2013 |
| 241 | 2^377799+52223 | 113729 | Yves Minet | 08/2010 |
| 242 | 11^109190-270 | 113710 | Enzo Doria | 12/2012 |
| 243 | 2^377222+93679 | 113556 | Yves Minet | 02/2011 |
| 244 | 35^73477-34^73477 | 113454 | Robert Price | 05/2012 |
| 245 | 2^376790+27 | 113426 | Lelio R Paula | 03/2013 |
| 246 | 2^376731+21 | 113408 | Lelio R Paula | 03/2013 |
| 247 | 2^375537+4847 | 113048 | Yves Minet | 02/2011 |
| 248 | 2^375350-3221 | 112992 | Yves Minet | 07/2011 |
| 249 | (29^77237-1)/28 | 112950 | Robert Price | 04/2012 |
| 250 | (2^374321+1)/3 | 112682 | H.&R. Lifchitz | 12/2000 |