Statistik: Fermatquotient  B^(P-1) == 1 (mod P^2)
Main table of content: http://www.fermatquotient.com/

Die Top 160 der bisher entdeckten Fermatquotienten ohne Primbasen (without prime base) <= 1052:
Basis Primzahl (Entdeckungsjahr)
770 194092950328757 (2024)
963 185422197633461 (2024)
852 179290250382637 (2023)
1023 162857063428079 (2022)
655 158039872478141 (2022)
447 146326546396711 (2021)
948 140030971047007 (2021)
970 137893087979557 (2021)
438 130424397928207 (2020)
70 119079791436527 (2020)
915 98985693983999 (2019)
897 92896514864623 (2018)
436 88556282027663 (2020)
524 87702160913599 (2020)
754 87185343382273 (2017)
492 85750417002241 (2017)
549 83997567503807 (2017)
856 83943401059799 (2019)
999 83815456559981 (2017)
731 82300301372323 (2017)
155 77322074223833 (2016)
889 73547302792739 (2019)
221 73446186360011 (2016)
700 65442059485993 (2015)
654 61515814197403 (2019)
485 60037905066809 (2019)
892 59773413984091 (2025)
805 59098152210389 (2015)
1041 54934609033817 (2024)
556 54930985557421 (2018)
[15686614387862 51504661351459 (2024)]
[21041566787583 51504661351459 (2024)]
[26033846849718 51504661351459 (2024)]
837 50998592653399 (2014)
177 49203761507753 (2014)
168 47955919706207 (2014)
1034 47726604579847 (2014)
707 47679740053003 (2017)
390 46950035940827 (2013)
935 41007656409263 (2013)
845 40987021669961 (2013)
445 40768330434331 (2016)
835 39628173693533 (2022)
[2025345309745 39453473334461 (2022)]
[6896158715012 39453473334461 (2022)]
588 37497252977117 (2012)
493 36843957223351 (2012)
388 36826068382487 (2016)
792 36313481871019 (2012)
494 34997771583587 (2012)
392 33906467435779 (2012)
747 32799228019681 (2015)
447 27856194112771 (2014)
895 26718272312891 (2021)
658 26213234261509 (2011)
458 25185917998729 (2020)
930 24287395851751 (2010)
814 22863373360561 (2010)
215 21451970877283 (2010)
228 20866199378047 (2010)
399 20125846752871 (2010)
168 19145241526811 (2010)
615 18895408512917 (2010)
1027 18639957895541 (2011)
868 16917592332617 (2009)
[11731011943922 16475012840609 (2019)]
403 16296551797663 (2009)
620 15145894824163 (2009)
768 14847328283687 (2009)
51 14802884210119 (2009)
[9984769265225 14802884210119 (2009)]
110 14438374183481 (2009)
[2704058032875 14438374183481 (2009)]
[6078809438104 14438374183481 (2009)]
[1608456660298 14034413930219 (2019)]
[10452184574303 14034413930219 (2019)]
[11581873404764 14034413930219 (2019)]
360 13842663034709 (2009)
[6319022671788 13842663034709 (2009)]
[13616429970784 13842663034709 (2009)]
[8147024755195 13368932516573 (2009)]
422 12757769381173 (2019)
910 12342837395351 (2009)
402 11174868949217 (2010)
713 11097981800233 (2008)
551 10781849409623 (2008)
989 10577489843279 (2008)
[2410017507347 10052723287699 (2012)]
415 9810493996903 (2009)
22 9809862296159 (2008)
[4376017644649 9809862296159 (2009)]
[6065078091938 9809862296159 (2009)]
872 9714810872587 (2009)
594 8784820622857 (2008)
890 8179693110613 (2009)
489 8157059583047 (2011)
273 7558891900249 (2007)
755 7334497678121 (2011)
478 7284323232409 (2011)
884 7196186279251 (2007)
40 7036306088681 (2007)
60 6683052151409 (2007)
[2264013798892 6683052151409 (2009)]
302 6681086808797 (2011)
321 6628000247353 (2009)
455 6617214825917 (2007)
575 6501209375021 (2007)
286 6489382948837 (2007)
758 6369167671939 (2011)
999 5879307404213 (2007)
964 5871394053781 (2011)
78 5744393199187 (2007)
[2161608938045 5744393199187 (2009)]
[3322314150128 5744393199187 (2009)]
[2889916318168 5025104010547 (2010)]
666 4977652953109 (2007)
134 4962859085059 (2009)
[4393169855999 4962859085059 (2009)]
750 4888164324599 (2007)
451 4855900311901 (2007)
298 4809986918441 (2009)
266 4673329018717 (2007)
669 4663313116307 (2010)
666 4503454574621 (2007)
370 4436281892011 (2007)
284 4019853486967 (2008)
[920073049032 3761059801469 (2010)]
737 3684324840109 (2008)
620 3533794899013 (2007)
604 3294062720537 (2010)
636 3258471060043 (2006)
590 3219042433511 (2006)
1030 3105232218721 (2008)
1014 2957593441709 (2006)
844 2943803595533 (2009)
334 2887182434861 (2009)
770 2771298845851 (2006)
322 2768017244933 (2006)
242 2706669242327 (2006)
945 2705324826961 (2006)
789 2307345676481 (2009)
1032 2281292790859 (2006)
830 2261347020859 (2007)
498 2149153512589 (2007)
650 2135417656303 (2006)
815 2030845176271 (2008)
393 1845595127527 (2007)
[386389357290 1822333408543 (2009)]
[974183630554 1822333408543 (2009)]
[1425799713522 1822333408543 (2009)]
958 1813979414189 (2008)
362 1794830107009 (2008)
910 1514654268719 (2006)
415 1465092947347 (2007)
508 1311889799369 (2007)
508 1274084375749 (2006)
758 1272207150661 (2007)
74 1251922253819 (2006)
[41768194945 1251922253819 (2009)]
363 1249344562091 (2006)
816 1241086902527 (2006)
110 1219715607577 (2006)
[347914584477 1219715607577 (2009)]
[650390161812 1219715607577 (2009)]
[685274994103 1219715607577 (2009)]
221 1180548631831 (2006)
973 1108107413579 (2006)
1008 1085992774211 (2006)
[406131698939 1082305363079 (2009)]
55 902060958301 (2005)
392 883201742719 (2005)
951 848378279311 (2007)
234 817766595407 (2006)
542 810202662271 (2016)
999 806812352251 (2006)
715 781059256409 (2006)
42 719867822369 (2005)
918 693582176263 (2006)
436 677213275049 (2006)
248 668677573093 (2006)
84 663840051067 (2005)
[339683704554 663840051067 (2009)]
395 651742019113 (2006)
960 644232442639 (2006)
935 626872115449 (2006)
87 604807523183 (2005)
[322994504180 604807523183 (2009)]
1030 594835481101 (2006)
66 588024812497 (2005)
[407916174766 588024812497 (2009)]
785 559491826637 (2006)
497 505780258937 (2006)
248 502608046943 (2006)
215 502095466241 (2006)

Die Top 193 der bisher entdeckten Fermatquotienten nur mit Primbasen (only prime base):
Primbasis Primzahl (Entdeckungsjahr)
[850699212818669 119079791436527 (2020)]
[994856726872367 119079791436527 (2020)]
349 51504661351459 (2024)
[92532419896141 51504661351459 (2024)]
[1313699693572261 51504661351459 (2024)]
853 39453473334461 (2022)
[989159636718109 39453473334461 (2022)]
[996628969731359 39453473334461 (2022)]
59 18088417183289 (2010)
197 16475012840609 (2019)
[132864958594657 16475012840609 (2019)]
[183482977102543 16475012840609 (2019)]
[208643815152109 16475012840609 (2019)]
[437119768319263 16475012840609 (2019)]
[275115089341061 14802884210119 (2009)]
[62634044602867 14438374183481 (2009)]
[88716895412501 14438374183481 (2009)]
347 14034413930219 (2019)
43 13368932516573 (2009)
[75933088226453 13368932516573 (2009)]
191 11055229853299 (2012)
[133862299160449 11055229853299 (2012)]
[146522401411117 11055229853299 (2012)]
877 10052723287699 (2012)
[41811115853113 9809862296159 (2009)]
379 9308580172669 (2012)
[82097854167971 9308580172669 (2012)]
79 8206949094581 (2009)
[105436981651843 8206949094581 (2009)]
[298828339911527 7036306088681 (2009)]
[222056571273569 6683052151409 (2009)]
619 6162516725413 (2011)
[176412925948901 5744393199187 (2009)]
641 5025104010547 (2010)
[38242878244763 5025104010547 (2010)]
[38854443073613 5025104010547 (2010)]
[56180208190163 5025104010547 (2010)]
[80511447209203 4962859085059 (2009)]
229 3761059801469 (2010)
[33306245226211 3761059801469 (2010)]
1049 3574693731373 (2010)
8387 3313684117619 (2025)
[41359271254429 3313684117619 (2025)]
[84563036699279 3313684117619 (2025)]
[88705327712047 3313684117619 (2025)]
5987 3197388605063 (2024)
[42925287617483 3197388605063 (2024)]
5303 3126943344193 (2024)
1447 3116563055779 (2024)
[51922001020361 3116563055779 (2024)]
4657 3047729645953 (2024)
[57628377907081 3047729645953 (2024)]
5407 2944255766321 (2024)
[63899595737311 2944255766321 (2024)]
7717 2934084419429 (2024)
3527 2812051483349 (2024)
6947 2798255058163 (2024)
[23054460691777 2798255058163 (2024)]
[44951816014747 2798255058163 (2024)]
5869 2798077034063 (2024)
[1126861912151 2798077034063 (2024)]
[11274957663311 2798077034063 (2024)]
1637 2759639135983 (2024)
[28722907532911 2759639135983 (2024)]
[31337420634281 2759639135983 (2024)]
6563 2746177254437 (2024)
[36469874427227 2746177254437 (2024)]
[54373211396773 2746177254437 (2024)]
4397 2709573967613 (2024)
[51241827600157 2709573967613 (2024)]
2477 2680164275143 (2024)
[47179638215821 2680164275143 (2024)]
[73106926091371 2680164275143 (2024)]
5623 2623424842849 (2024)
[45848409722779 2623424842849 (2024)]
5879 2620993476611 (2024)
[11981262230299 2620993476611 (2024)]
[74598265532443 2620993476611 (2024)]
769 2586456935177 (2009)
[67281861620969 2586456935177 (2009)]
1559 2585281879729 (2024)
[19268826448903 2585281879729 (2024)]
[40748647327807 2585281879729 (2024)]
23 2549536629329 (2006)
[19925360452639 2549536629329 (2009)]
[54365062168699 2549536629329 (2009)]
8753 2523578764589 (2024)
[26557658258683 2523578764589 (2024)]
3581 2482723444781 (2024)
6359 2438720252923 (2024)
8969 2422564458581 (2024)
[2441923948699 2422564458581 (2024)]
[27173724200611 2422564458581 (2024)]
6173 2333144195059 (2024)
[570720914677 2333144195059 (2024)]
3463 2266698862711 (2024)
[3459294539693 2266698862711 (2024)]
[10708078197347 2266698862711 (2024)]
[17785913712313 2266698862711 (2024)]
[41668784023739 2266698862711 (2024)]
1933 2231978166101 (2023)
[7010092212719 2231978166101 (2023)]
3433 2215925784269 (2023)
[34927842089369 2215925784269 (2023)]
7753 2198812259219 (2023)
2281 2152199829413 (2023)
[27074487946907 2152199829413 (2023)]
5701 2136890336159 (2023)
2857 2042237139779 (2023)
4127 2013560269213 (2023)
[18591086134997 2013560269213 (2023)]
[53300299505963 2013560269213 (2023)]
2053 2005365019123 (2023)
2143 1988317613923 (2023)
[43476260429659 1988317613923 (2023)]
6569 1926547427591 (2023)
[11912616627427 1926547427591 (2023)]
[12890268884329 1926547427591 (2023)]
[42753004240391 1926547427591 (2023)]
8363 1921307884511 (2023)
[8217615685387 1921307884511 (2023)]
[8912269705121 1921307884511 (2023)]
[25480135630921 1921307884511 (2023)]
7901 1888395760243 (2023)
1801 1852474354673 (2023)
[2921806898977 1852474354673 (2023)]
4021 1851516773377 (2023)
139 1822333408543 (2007)
[18571426512689 1822333408543 (2009)]
6709 1729909359859 (2023)
[2829311063923 1729909359859 (2023)]
[11775563195717 1729909359859 (2023)]
7331 1722704779141 (2023)
9629 1715991126271 (2023)
[12103963103753 1715991126271 (2023)]
[18326539722121 1715991126271 (2023)]
[30827340975961 1715991126271 (2023)]
6121 1711708697057 (2023)
[23414592491057 1711708697057 (2023)]
7507 1668073671619 (2023)
1553 1660850494801 (2023)
[38403523209167 1660850494801 (2023)]
4441 1497438163657 (2023)
[26428404866569 1497438163657 (2023)]
[28636950856951 1497438163657 (2023)]
5437 1491820282727 (2023)
8263 1463513370667 (2023)
5113 1380407886251 (2023)
9203 1339121083693 (2023)
8699 1285238295343 (2022)
3457 1248726360187 (2022)
[1331792551781 1248726360187 (2023)]
[21306191772703 1248726360187 (2023)]
[27479343501059 1248726360187 (2023)]
[32037779061289 1248726360187 (2023)]
8839 1211653344311 (2022)
421 1083982004309 (2007)
[15688082687801 1083982004309 (2009)]
953 1082305363079 (2007)
9137 1056305858813 (2017)
3313 1013674942057 (2017)
6113 1000436194319 (2017)
3037 988813725773 (2017)
[16130108550599 988813725773 (2017)]
[24357707026619 988813725773 (2017)]
[38688816580241 902060958301 (2009)]
1453 899047722887 (2016)
2729 891336031823 (2016)
9319 873721154437 (2016)
[4010065734061 873721154437 (2016)]
4549 849961437053 (2016)
5303 821924415181 (2016)
[11728465894063 821924415181 (2016)]
[13951421681177 821924415181 (2016)]
8837 814523545037 (2016)
[1502836338869 814523545037 (2016)]
[20848544916631 814523545037 (2016)]
6481 793214324801 (2015)
[2397499394989 793214324801 (2016)]
[12701603092487 793214324801 (2016)]
3761 775472594399 (2015)
[1922088952027 719867822369 (2009)]
2699 716486626979 (2015)
6907 709456324673 (2015)
[6040115481791 709456324673 (2015)]
[7569277378699 709456324673 (2015)]
9277 689140261499 (2015)
[10980596353187 689140261499 (2015)]
[15227174356127 689140261499 (2015)]
[18055078582043 689140261499 (2015)]
1423 681205498439 (2015)
6863 679020881137 (2015)
[8367752562157 663840051067 (2009)]
5857 660514639529 (2015)
[3452027330933 660514639529 (2015)]
[9512481380089 660514639529 (2015)]
[11567031887903 660514639529 (2015)]
[17185379147749 660514639529 (2015)]
6577 646667972609 (2015)
5399 634273823383 (2015)
7877 620610408269 (2015)
[8121617365579 620610408269 (2015)]
2713 612278081209 (2014)
[4405930606531 612278081209 (2014)]
1249 608113804939 (2014)
[11957109174251 608113804939 (2014)]
[15746586862207 608113804939 (2014)]
1637 604883665297 (2014)
[12351961021567 604883665297 (2014)]
9533 594818875289 (2014)
[3384775307663 594818875289 (2014)]
1861 585825432611 (2014)
[9440577678097 585825432611 (2014)]
5309 580593350849 (2014)
9013 552506659391 (2014)
[3376691505881 552506659391 (2014)]
8521 551362258487 (2014)
[9448265810861 551362258487 (2014)]
7877 529850079383 (2014)
[5818675703927 529850079383 (2014)]
[9981693752089 529850079383 (2014)]
8521 522708051857 (2014)
[12955921378423 522708051857 (2014)]
1697 515504206849 (2014)
[890172416821 515504206849 (2014)]
3319 510272063849 (2014)
5171 508761983809 (2014)
[7036533672109 508761983809 (2014)]
7121 505555659551 (2014)
[1111156284781 505555659551 (2014)]
7927 504500378099 (2014)
[591648095587 504500378099 (2014)]
[7237281747197 504500378099 (2014)]
1103 497833887919 (2014)
1889 490741538587 (2014)
[1459464786947 490741538587 (2014)]
4441 479893678123 (2014)
17 478225523351 (2005)
[2227246108447 478225523351 (2006)]
[5079946164589 478225523351 (2006)]
661 462147547073 (2006)
[5287036584811 462147547073 (2009)]
3037 442958275769 (2013)
[201406395977 442958275769 (2013)]
3001 430718502983 (2013)
[1143379871261 430718502983 (2013)]
[9704957832797 430718502983 (2013)]
[9896430591001 430718502983 (2013)]
7577 419749976447 (2013)
[2950496678719 419749976447 (2013)]
8861 413636372647 (2013)
[7378822665013 413636372647 (2013)]
8819 405838367191 (2013)
[7600788379237 405838367191 (2013)]
[8195966832407 405838367191 (2013)]
113 405697846751 (2005)
[1918967153837 405697846751 (2009)]
8117 404824295269 (2013)
[3657353507053 404824295269 (2013)]
[5350205822713 404824295269 (2013)]
[9809408700601 404824295269 (2013)]
1493 400457765437 (2013)
[5982583290947 400457765437 (2013)]
5087 392265093887 (2013)
[1067660188261 392265093887 (2013)]
[9668908556851 392265093887 (2013)]
3461 378945674369 (2013)
[9873598138697 378945674369 (2013)]
2687 356006523907 (2013)
[2619294905819 356006523907 (2013)]
[4461427706227 356006523907 (2013)]
9209 353622278099 (2013)
[2593089749099 353622278099 (2013)]
9623 334729063309 (2013)
[7104785301241 334729063309 (2013)]
5051 334428325993 (2013)
[6006883283183 334428325993 (2013)]
8209 327742840109 (2013)
[1829701997177 327742840109 (2013)]
1123 320902921541 (2013)
[4942200141533 320902921541 (2013)]
[5812080944617 320902921541 (2013)]
691 312679516579 (2006)
[64907851831 312679516579 (2009)]
[77658868919 312679516579 (2009)]
[235522640761 312679516579 (2009)]
9767 306871823327 (2013)
[300007611181 306871823327 (2013)]
9461 298069561501 (2013)
7331 297095539969 (2013)
[6061857371741 297095539969 (2013)]
2969 296588541479 (2013)
[262398477619 296588541479 (2013)]
[5597254171387 296588541479 (2013)]
4441 293759060339 (2013)
5171 292122064649 (2013)
2143 290970625471 (2013)
[591099707377 290970625471 (2013)]
9323 287014977877 (2012)
[7037472280963 287014977877 (2012)]
3187 279940802563 (2012)
3769 279342238649 (2012)
[301254375161 279342238649 (2012)]
[3308046136799 279342238649 (2012)]
[3533725068241 279342238649 (2012)]
[4933736031619 279342238649 (2012)]
7703 278643506767 (2012)
157 275318049829 (2006)
6841 263923015819 (2012)
5647 263068392641 (2012)
[3051353732551 263068392641 (2012)]
5939 259632690041 (2012)
[361826615431 259632690041 (2012)]
[2015481863579 259632690041 (2012)]
[3848670149843 259632690041 (2012)]
[4897444703869 259632690041 (2012)]
4451 255584551553 (2012)
277 243547988443 (2006)
[182518719407 243547988443 (2009)]
5881 239395030153 (2012)
[4634897377027 239395030153 (2012)]
4549 237941349733 (2012)
[1389627425701 237941349733 (2012)]
8443 237661573661 (2012)
[3966687615677 237661573661 (2012)]
4793 229517991499 (2012)
2749 229337011213 (2012)
[3029801641309 225413072431 (2009)]
953 220564434997 (2006)
8527 201340257421 (2012)
6173 194087048317 (2012)
9343 194020244069 (2012)
[2999893544213 194020244069 (2012)]
9371 193470361663 (2012)
7177 189637752053 (2012)
[2360253166597 189637752053 (2012)]
5 188748146801 (1997, Discoverer Wilfrid Keller)
7639 179209138811 (2012)
2081 176528344417 (2012)
1871 173235298889 (2012)
7741 157382897233 (2012)
[545271203297 157382897233 (2012)]
7451 152100787987 (2012)
[336840301367 152100787987 (2012)]
1021 144682870477 (2006)
[1283047752499 144682870477 (2009)]
[1735840012091 144682870477 (2009)]
3037 144020304347 (2012)
[640909982311 144020304347 (2012)]
9587 136555727311 (2012)
5531 135127009471 (2012)
[1513490828821 135127009471 (2012)]
[2057372106877 135127009471 (2012)]
[2160011769913 135127009471 (2012)]
[2650314290993 135127009471 (2012)]
3889 130873091287 (2012)
[2352609864331 130873091287 (2012)]
7451 129557399941 (2012)
[199800787159 129557399941 (2012)]
1571 128920748543 (2012)
10009 128320252987 (2012)
8111 128031864581 (2012)
2473 123416538821 (2011)
[2905846429511 123416538821 (2012)]
7177 122067595081 (2011)
[2249546331673 122067595081 (2011)]
9743 121734577919 (2011)
[299292249563 121734577919 (2011)]
[1949177551481 121734577919 (2011)]
491 121261604419 (2006)
[1015823793011 121261604419 (2009)]
[487360026007 119327070011 (2006)]
[1792352470627 119327070011 (2006)]
[1104815768579 115755260963 (2006)]
6709 113811486757 (2011)
7577 111594280579 (2011)
10111 105988925209 (2011)
[27228892879 105988925209 (2011)]
[3419895391051 103336004179 (2006)]
[1718271230393 103053130679 (2009)]
6311 102249119591 (2011)
4483 97780315427 (2011)
[2184944902103 96185643031 (2006)]
[1098129621247 94727075783 (2006)]
881 94626144313 (1998, Discoverer Joerg Richstein)
4397 87628917119 (2011)
[146060500379 87628917119 (2011)]
9203 84011448791 (2011)
8461 79132195127 (2011)
9677 76759955329 (2008, Discoverer Michael Mossinghoff)
[332185011343 76759955329 (2010)]
[501254582893 76759955329 (2010)]
97 76704103313 (1998, Discoverer Joerg Richstein)
[236917183271 76704103313 (2006)]
37 76407520781 (1998, Discoverer Joerg Richstein)
3727 75759534919 (2011)
6221 74235431771 (2011)
[449703460081 74235431771 (2011)]
8377 73948637123 (2011)
7127 72320415737 (2011)
2879 71904042853 (2011)
1429 70914097931 (2011)
[140817583999 70914097931 (2011)]

Vergleich zu meinen berechneten Erwartungswerten (expectation values) bei P^2
Fehler = (Ist - Erwartungswert) / Wurzel(Erwartungswert)
Error = (effective - expectation) / Sqrt(expectation)
133 Basen von 2 bis 150
von bis Erwartungswert Ist Fehler
10^2 10^3 51.9 42 -1.4
10^3 10^4 37.9 36 -0.3
10^4 10^5 29.6 40 +1.9
10^5 10^6 24.2 19 -1.1
10^6 10^7 20.5 18 -0.6
10^7 10^8 17.8 22 +1.0
10^8 10^9 15.7 10 -1.4
10^9 10^10 14.0 19 +1.3
10^10 10^11 12.7 13 +0.1
10^11 10^12 11.6 13 +0.4
10^12 10^13 10.6 10 -0.2
10^13 1.997E+14 12.7 5 -2.2

877 Basen von 151 bis 1052
von bis Erwartungswert Ist Fehler
10^2 10^3 342.2 368 +1.4
10^3 10^4 249.6 256 +0.4
10^4 10^5 194.9 193 -0.1
10^5 10^6 159.7 184 +1.9
10^6 10^7 135.2 151 +1.4
10^7 10^8 117.1 121 +0.4
10^8 10^9 103.3 103 -0.0
10^9 10^10 92.4 74 -1.9
10^10 10^11 83.6 90 +0.7
10^11 10^12 76.3 75 -0.1
10^12 10^13 70.2 66 -0.5
10^13 6.06E+13 51.3 51 -0.0

Anzahl der zu erwartenden Fermatquotienten bis zu einer extrem grossen Zahl x
Durchschnitt aller Basen: ln[ln(x)] - 0.190750207193422...
Durchschnitt bei sehr grossen Primbasen: ln[ln(x)] + 0.261497212847642...
Durchschnitt ohne die trivialen Fermatquotienten: ln[ln(x)] - 0.845245047275553...
Unter "trivial" verstehe ich hier diejenigen Fermatquotienten, die man ohne Suchen 
vorhersagen kann. Dies gilt bei den Basen B = i*P^2 ± 1 mit Ausnahme der Primzahl 
P=2 bei i*2^2-1.
Beispiel: Primzahl 103
Diese Zahl ist als Formatquotient trivial fuer die Basen 103^2±1, 2*103^2±1, 3*103^2±1, ...
Also fuer B = 10608, 10610, 21217, 21219, 31826, 31828, ...

Ueberraschend grosse Luecke zwischen den Fermatquotienten bei der Suche bis zur Basis 
1052. Vor der Luecke:
Basis: 413 P: 2832308863
Basis: 799 P: 2891032049
Basis: 723 P: 2938943531
Luecke mit Merit 13.581 = [ln(ln 3947883749) - ln(ln 2938943531)] * 1010 (gute Naeherung)
Statistisch kommt eine solche Luecke im Durchschnitt nur alle rund 790000 Quotienten vor.
Nach der Luecke:
Basis: 738 P: 3947883749
Basis: 260 P: 3977977109
Basis: 147 P: 4058948753

Extreme Naehe:
Basis: 994 P: 5431
Basis: 994 P: 5449
Basis: 1015 P: 22853
Basis: 1015 P: 23339
Basis: 252 P: 394213789
Basis: 251 P: 395696461
Basis: 501 P: 24112920253
Basis: 499 P: 24117560837
Basis: 220 P: 32376410527
Basis: 220 P: 34816906301
Basis: 508 P: 1274084375749
Basis: 508 P: 1311889799369
Basis: 666 P: 4503454574621
Basis: 666 P: 4977652953109
Basis: 494 P: 34997771583587
Basis: 493 P: 36843957223351
Basis: 556 P: 54930985557421
Basis: 1041 P: 54934609033817

Nur unterschiedliche Basis:
Basis: 391 P: 68903
Basis: 767 P: 68903
Basis: 371 P: 101113
Basis: 1010 P: 101113

Nur vertauschte Ziffern in den Primzahlen:
Basis: 457 P: 1589513
Basis: 22 P: 1595813


Die Fermatquotienten 1093 und 3511 bei der Basis 2 haben einen speziellen Namen, die 
Wieferich primes.
Trotz intensiver Suche hat man bis heute keine 3. Wieferich-Primzahl gefunden.
Aktueller Stand siehe:  http://u-g-f.de/PRPNet/findlist_adv.php?proj=WFS
Unter der Adresse  http://www.loria.fr/~zimmerma/records/Wieferich.status sind die 
beiden beinahe Wieferich-Primzahlen 47004625957 und 76843523891 zu finden. Um bei der 
heutigen Ausgangslage (bis 6E+17) nach meiner Berechnung einen Erwartungswert von 1 
zu haben, muesste man bis 2.12E+48 weitersuchen. Trotzdem gehe ich entgegen der heutigen 
Meinung, davon aus, dass es unendlich viele Wieferich-Primzahlen gibt.
Dass es pro Groessenordung tendenziell immer weniger Fast-Wieferich-Primzahlen gibt, 
faellt ja mit der Ableitung von ln[ln(x)] respektive mit der Primzahldichte zusammen.

05.03.2025  Richard Fischer