Quelltext der Seite PrimeGrid/Proth Prime Search

'''Proth Prime Search''' sucht nach Primzahlen der Form '''''k''&#8729;2<sup>''n''</sup>+1''' mit 2<sup>''n''</sup> > ''k'' und ''k'' ungerade. Jede Primzahl lässt sich eindeutig in der Form ''k''&#8729;2<sup>''n''</sup>+1 schreiben, aber damit die Primzahl eine Prothsche Primzahl ist, muss zusätzlich 2<sup>''n''</sup> > k gelten.

Jede Prothsche Primzahl kann Teiler von Fermatzahlen (F<sub>''n''</sub> = 2<sup>2<sup>''n''</sup></sup>+1), verallgemeinerten Fermatzahlen (GF(''n'', ''b'') = ''b''<sup>2<sup>''n''</sup></sup>+1) oder erweiterten verallgemeinerten Fermatzahlen (xGF(''n'', ''a'', ''b'') = ''a''<sup>2<sup>''n''</sup></sup>+''b''<sup>2<sup>''n''</sup></sup>) sein. Deshalb wird jede bei diesem Projekt gefundene Primzahl auf diese Eigenschaften getestet.

{{PGSubprojekt
|Status=<span style="color:#00ff00;">'''aktiv'''</span>
|Homepage=http://prothsearch.com/
|Beginn=April 1998
|PGBeginn=27. Februar 2008
|PGForum=http://www.primegrid.com/forum_forum.php?id=36
|Suchbereich=1 < ''n'' < 5M (4 < ''k'' < 1200)<br>1 < ''n'' < 2M (1200 < ''k'' < 10000)
|App=
|AppBadge=
|Sieve='''PPS Sieve''' (via BOINC)
|SieveBadge=sr2sieve_pps
|Primtest='''LLR''' (via BOINC)
|PrimtestBadge=pps_llr
|SGForum=<vbthread id=4320>Proth Prime Search</vbthread>}}
==Funde==
'''651&sdot;2<sup>476632</sup>+1''' teilt F<sub>476624</sub> (27.12.2008; 143484 Stellen, [https://www.primegrid.com/download/PPS-F476624.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=86060 Prime Pages])<br>
'''519&sdot;2<sup>567235</sup>+1''' teilt F<sub>567233</sub> (06.03.2009; 170758 Stellen, [https://www.primegrid.com/download/PPS-F567233.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=87008 Prime Pages])<br>
'''659&sdot;2<sup>617815</sup>+1''' teilt F<sub>617813</sub> (31.03.2009; 185984 Stellen, [https://www.primegrid.com/download/PPS-F617815.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=87401 Prime Pages])<br>
'''7333&sdot;2<sup>138560</sup>+1''' teilt F<sub>138557</sub> (12.03.2011; 41715 Stellen, [https://www.primegrid.com/download/PPS-F138557.pdf Bekanntgabe])<br>
'''9&sdot;2<sup>2543551</sup>+1''' teilt F<sub>2543548</sub> (22.06.2011; 765687 Stellen, [https://www.primegrid.com/download/PPS-F2543548.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=100563 Prime Pages])<br>
'''3771&sdot;2<sup>221676</sup>+1''' teilt F<sub>221670</sub> (01.07.2011; 66736 Stellen, [https://www.primegrid.com/download/PPS-F221670.pdf Bekanntgabe])<br>
'''4479&sdot;2<sup>226618</sup>+1''' teilt F<sub>226614</sub> (08.07.2011; 68223 Stellen, [https://www.primegrid.com/download/PPS-F226614.pdf Bekanntgabe])<br>
'''25&sdot;2<sup>2141884</sup>+1''' teilt F<sub>2141872</sub> (09.09.2011; 644773 Stellen, [https://www.primegrid.com/download/PPS-F2141884.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=101943 Prime Pages])<br>
'''329&sdot;2<sup>1246017</sup>+1''' teilt F<sub>1246013</sub> (04.01.2012; 375092 Stellen, [https://www.primegrid.com/download/PPS-F1246013.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=103866 Prime Pages])<br>
'''81&sdot;2<sup>3352924</sup>+1''' (17.01.2012; 1009333 Stellen, [https://www.primegrid.com/download/mega-3352924.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=103953 Prime Pages])<br>
'''131&sdot;2<sup>1494099</sup>+1''' teilt F<sub>1494096</sub> (07.02.2012; 449771 Stellen, [https://www.primegrid.com/download/PPS-F1494096.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=104247 Prime Pages])<br>
'''7905&sdot;2<sup>352281</sup>+1''' teilt F<sub>352279</sub> (02.05.2012; 106052 Stellen, [https://www.primegrid.com/download/PPS-F352279.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=107379 Prime Pages])<br>
'''1705&sdot;2<sup>906110</sup>+1''' teilt F<sub>906108</sub> (13.06.2012; 272770 Stellen, [https://www.primegrid.com/download/PPS-F906108.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=107685 Prime Pages])<br>
'''9&sdot;2<sup>3497442</sup>+1''' (23.10.2012; 1052836 Stellen, [https://www.primegrid.com/download/PPS-3497442.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=109930 Prime Pages])<br>
'''7&sdot;2<sup>5775996</sup>+1''' (02.11.2012; 1738749 Stellen, [https://www.primegrid.com/download/PPS-5775996.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=110070 Prime Pages])<br>
'''183&sdot;2<sup>1747660</sup>+1''' teilt F<sub>1747656</sub> (10.03.2013; 526101 Stellen, [https://www.primegrid.com/download/PPS-F1747656.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=111542 Prime Pages])<br>
'''57&sdot;2<sup>2747499</sup>+1''' teilt F<sub>2747497</sub> (13.05.2013; 827082 Stellen, [https://www.primegrid.com/download/PPS-2747497.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=114144 Prime Pages])<br>
'''2145&sdot;2<sup>1099064</sup>+1''' teilt F<sub>1099061</sub> (18.06.2013; 330855 Stellen, [https://www.primegrid.com/download/PPS-F1099061.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=114458 Prime Pages])<br>
'''87&sdot;2<sup>3496188</sup>+1''' (28.03.2014; 1052460 Stellen, [https://www.primegrid.com/download/mega-3496188.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=117520 Prime Pages])<br>
'''51&sdot;2<sup>3490971</sup>+1''' (28.03.2014; 1050889 Stellen, [https://www.primegrid.com/download/mega-3490971.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=117508 Prime Pages])<br>
'''93&sdot;2<sup>3544744</sup>+1''' (06.05.2014; 1067077 Stellen, [https://www.primegrid.com/download/mega-3544744.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=117797 Prime Pages])<br>
'''33&sdot;2<sup>3570132</sup>+1''' (10.06.2014; 1074719 Stellen, [https://www.primegrid.com/download/mega-3570132.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118003 Prime Pages])<br>
'''35&sdot;2<sup>3570777</sup>+1''' (10.06.2014; 1074913 Stellen, [https://www.primegrid.com/download/mega-3570777.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118004 Prime Pages])<br>
'''35&sdot;2<sup>3587843</sup>+1''' (04.07.2014; 1080050 Stellen, [https://www.primegrid.com/download/mega-3587843.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118131 Prime Pages])<br>
'''129&sdot;2<sup>3328805</sup>+1''' (24.07.2014; 1002073 Stellen, [https://www.primegrid.com/download/mega-3328805.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118246 Prime Pages])<br>
'''193&sdot;2<sup>3329782</sup>+1''' teilt F<sub>3329780</sub> (25.07.2014; 1002367 Stellen, [https://www.primegrid.com/download/mega-3329782.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118254 Prime Pages])<br>
'''179&sdot;2<sup>3371145</sup>+1''' (23.09.2014; 1014819 Stellen, [https://www.primegrid.com/download/mega-3371145.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118611 Prime Pages])<br>
'''255&sdot;2<sup>3395661</sup>+1''' (01.12.2014; 1022199 Stellen, [https://www.primegrid.com/download/mega-3395661.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=118849 Prime Pages])<br>
'''177&sdot;2<sup>3411847</sup>+1''' (06.01.2015; 1027071 Stellen, [https://www.primegrid.com/download/mega-3411847.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119060 Prime Pages])<br>
'''245&sdot;2<sup>3411973</sup>+1''' (07.01.2015; 1027109 Stellen, [https://www.primegrid.com/download/mega-3411973.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119066 Prime Pages])<br>
'''159&sdot;2<sup>3425766</sup>+1''' (01.02.2015; 1031261 Stellen, [https://www.primegrid.com/download/mega-3425766.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119192 Prime Pages])<br>
'''267&sdot;2<sup>2662090</sup>+1''' teilt F<sub>2662088</sub> (13.02.2015; 801372 Stellen, [https://www.primegrid.com/download/PPS-F2662088.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119333 Prime Pages])<br>
'''113&sdot;2<sup>3437145</sup>+1''' (14.02.2015; 1034686 Stellen, [https://www.primegrid.com/download/mega-3437145.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119330 Prime Pages])<br>
'''197&sdot;2<sup>3477399</sup>+1''' (19.04.2015; 1046804 Stellen, [https://www.primegrid.com/download/mega-3477399.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119777 Prime Pages])<br>
'''249&sdot;2<sup>3486411</sup>+1''' (10.05.2015; 1049517 Stellen, [https://www.primegrid.com/download/mega-3486411.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119905 Prime Pages])<br>
'''195&sdot;2<sup>3486379</sup>+1''' (10.05.2015; 1049507 Stellen, [https://www.primegrid.com/download/mega-3486379.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=119904 Prime Pages])<br>
'''135&sdot;2<sup>3518338</sup>+1''' (02.08.2015; 1059128 Stellen, [https://www.primegrid.com/download/mega-3518338.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=120186 Prime Pages])<br>
'''141&sdot;2<sup>3529287</sup>+1''' (01.09.2015; 1062424 Stellen, [https://www.primegrid.com/download/mega-3529287.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=120306 Prime Pages])<br>
'''191&sdot;2<sup>3548117</sup>+1''' (30.10.2015; 1068092 Stellen, [https://www.primegrid.com/download/mega-3548117.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=120499 Prime Pages])<br>
'''251&sdot;2<sup>3574535</sup>+1''' (25.01.2016; 1076045 Stellen, [https://www.primegrid.com/download/mega-3574535.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=120932 Prime Pages])<br>
'''275&sdot;2<sup>3585539</sup>+1''' (09.02.2016; 1079358 Stellen, [https://www.primegrid.com/download/mega-3585539.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121092 Prime Pages])<br>
'''387&sdot;2<sup>3322763</sup>+1''' (21.02.2016; 1000254 Stellen, [https://www.primegrid.com/download/mega-3322763.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121243 Prime Pages])<br>
'''189&sdot;2<sup>3596375</sup>+1''' (24.02.2016; 1082620 Stellen, [https://www.primegrid.com/download/mega-3596375.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121287 Prime Pages])<br>
'''393&sdot;2<sup>3349525</sup>+1''' (24.03.2016; 1008311 Stellen, [https://www.primegrid.com/download/mega-3349525.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121472 Prime Pages])<br>
'''369&sdot;2<sup>3365614</sup>+1''' (10.04.2016; 1013154 Stellen, [https://www.primegrid.com/download/mega-3365614.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121546 Prime Pages])<br>
'''303&sdot;2<sup>3391977</sup>+1''' (09.05.2016; 1021090 Stellen, [https://www.primegrid.com/download/mega-3391977.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121647 Prime Pages])<br>
'''373&sdot;2<sup>3404702</sup>+1''' (16.05.2016; 1024921 Stellen, [https://www.primegrid.com/download/mega-3404702.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121663 Prime Pages])<br>
'''323&sdot;2<sup>3482789</sup>+1''' (20.06.2016; 1048427 Stellen, [https://www.primegrid.com/download/mega-3482789.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121815 Prime Pages])<br>
'''329&sdot;2<sup>3518451</sup>+1''' (21.06.2016; 1059162 Stellen, [https://www.primegrid.com/download/mega-3518451.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121817 Prime Pages])<br>
'''345&sdot;2<sup>3532957</sup>+1''' (22.06.2016; 1063529 Stellen, [https://www.primegrid.com/download/mega-3532957.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121819 Prime Pages])<br>
'''351&sdot;2<sup>3545752</sup>+1''' (22.06.2016; 1067381 Stellen, [https://www.primegrid.com/download/mega-3545752.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121821 Prime Pages])<br>
'''381&sdot;2<sup>3563676</sup>+1''' (23.06.2016; 1072776 Stellen, [https://www.primegrid.com/download/mega-3563676.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121825 Prime Pages])<br>
'''309&sdot;2<sup>3577339</sup>+1''' (24.06.2016; 1076889 Stellen, [https://www.primegrid.com/download/mega-3577339.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121826 Prime Pages])<br>
'''403&sdot;2<sup>3334410</sup>+1''' (25.06.2016; 1003716 Stellen, [https://www.primegrid.com/download/mega-3334410.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121829 Prime Pages])<br>
'''453&sdot;2<sup>3387048</sup>+1''' (14.07.2016; 1019606 Stellen, [https://www.primegrid.com/download/mega-3387048.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121899 Prime Pages])<br>
'''479&sdot;2<sup>3411975</sup>+1''' (25.07.2016; 1027110 Stellen, [https://www.primegrid.com/download/mega-3411975.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=121945 Prime Pages])<br>
'''453&sdot;2<sup>3461688</sup>+1''' (23.08.2016; 1042075 Stellen, [https://www.primegrid.com/download/mega-3461688.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122075 Prime Pages])<br>
'''491&sdot;2<sup>3473837</sup>+1''' (29.08.2016; 1045732 Stellen, [https://www.primegrid.com/download/mega-3473837.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122104 Prime Pages])<br>
'''495&sdot;2<sup>3484656</sup>+1''' (05.09.2016; 1048989 Stellen, [https://www.primegrid.com/download/mega-3484656.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122163 Prime Pages])<br>
'''447&sdot;2<sup>3533656</sup>+1''' (28.09.2016; 1063740 Stellen, [https://www.primegrid.com/download/mega-3533656.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122259 Prime Pages])<br>
'''465&sdot;2<sup>3536871</sup>+1''' (30.09.2016; 1064707 Stellen, [https://www.primegrid.com/download/mega-3536871.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122280 Prime Pages])<br>
'''415&sdot;2<sup>3559614</sup>+1''' (08.10.2016; 1071554 Stellen, [https://www.primegrid.com/download/mega-3559614.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122339 Prime Pages])<br>
'''597&sdot;2<sup>3322871</sup>+1''' (21.10.2016; 1000287 Stellen, [https://www.primegrid.com/download/mega-3322871.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122400 Prime Pages])<br>
'''791&sdot;2<sup>3323995</sup>+1''' (24.10.2016; 1000626 Stellen, [https://www.primegrid.com/download/mega-3323995.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122411 Prime Pages])<br>
'''555&sdot;2<sup>3325925</sup>+1''' (30.10.2016; 1001206 Stellen, [https://www.primegrid.com/download/mega-3325925.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122426 Prime Pages])<br>
'''821&sdot;2<sup>3327003</sup>+1''' (02.11.2016; 1001531 Stellen, [https://www.primegrid.com/download/mega-3327003.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122463 Prime Pages])<br>
'''659&sdot;2<sup>3327371</sup>+1''' (03.11.2016; 1001642 Stellen, [https://www.primegrid.com/download/mega-3327371.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122468 Prime Pages])<br>
'''655&sdot;2<sup>3327518</sup>+1''' (04.11.2016; 1001686 Stellen, [https://www.primegrid.com/download/mega-3327518.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122469 Prime Pages])<br>
'''673&sdot;2<sup>3330436</sup>+1''' (12.11.2016; 1002564 Stellen, [https://www.primegrid.com/download/mega-3330436.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122491 Prime Pages])<br>
'''611&sdot;2<sup>3334875</sup>+1''' (27.11.2016; 1003901 Stellen, [https://www.primegrid.com/download/mega-3334875.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122540 Prime Pages])<br>
'''849&sdot;2<sup>3335669</sup>+1''' (29.11.2016; 1004140 Stellen, [https://www.primegrid.com/download/mega-3335669.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122549 Prime Pages])<br>
'''651&sdot;2<sup>3337101</sup>+1''' (03.12.2016; 1004571 Stellen, [https://www.primegrid.com/download/mega-3337101.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122566 Prime Pages])<br>
'''733&sdot;2<sup>3340464</sup>+1''' (12.12.2016; 1005583 Stellen, [https://www.primegrid.com/download/mega-3340464.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122592 Prime Pages])<br>
'''543&sdot;2<sup>3351686</sup>+1''' (16.01.2017; 1008961 Stellen, [https://www.primegrid.com/download/mega-3351686.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122748 Prime Pages])<br>
'''1183&sdot;2<sup>3353058</sup>+1''' (19.01.2017; 1009375 Stellen, [https://www.primegrid.com/download/mega-3353058.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122771 Prime Pages])<br>
'''619&sdot;2<sup>3362814</sup>+1''' (09.02.2017; 1012311 Stellen, [https://www.primegrid.com/download/mega-3362814.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122904 Prime Pages])<br>
'''533&sdot;2<sup>3362857</sup>+1''' (09.02.2017; 1012324 Stellen, [https://www.primegrid.com/download/mega-3362857.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122908 Prime Pages])<br>
'''777&sdot;2<sup>3367372</sup>+1''' (17.02.2017; 1013683 Stellen, [https://www.primegrid.com/download/mega-3367372.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122971 Prime Pages])<br>
'''617&sdot;2<sup>3368119</sup>+1''' (18.02.2017; 1013908 Stellen, [https://www.primegrid.com/download/mega-3368119.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122988 Prime Pages])<br>
'''715&sdot;2<sup>3368210</sup>+1''' (18.02.2017; 1013936 Stellen, [https://www.primegrid.com/download/mega-3368210.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=122995 Prime Pages])<br>
'''677&sdot;2<sup>3369115</sup>+1''' (20.02.2017; 1014208 Stellen, [https://www.primegrid.com/download/mega-3369115.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123022 Prime Pages])<br>
'''839&sdot;2<sup>3369383</sup>+1''' (21.02.2017; 1014289 Stellen, [https://www.primegrid.com/download/mega-3369383.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123026 Prime Pages])<br>
'''861&sdot;2<sup>3377601</sup>+1''' (12.03.2017; 1016763 Stellen, [https://www.primegrid.com/download/mega-3377601.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123141 Prime Pages])<br>
'''1093&sdot;2<sup>3378000</sup>+1''' (14.03.2017; 1016883 Stellen, [https://www.primegrid.com/download/mega-3378000.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123149 Prime Pages])<br>
'''621&sdot;2<sup>3378148</sup>+1''' (14.03.2017; 1016927 Stellen, [https://www.primegrid.com/download/mega-3378148.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123150 Prime Pages])<br>
'''663&sdot;2<sup>3390469</sup>+1''' (23.04.2017; 1020636 Stellen, [https://www.primegrid.com/download/mega-3390469.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123311 Prime Pages])<br>
'''805&sdot;2<sup>3391818</sup>+1''' (28.04.2017; 1021042 Stellen, [https://www.primegrid.com/download/mega-3391818.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123322 Prime Pages])<br>
'''609&sdot;2<sup>3392301</sup>+1''' (29.04.2017; 1021188 Stellen, [https://www.primegrid.com/download/mega-3392301.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123380 Prime Pages])<br>
'''555&sdot;2<sup>3393389</sup>+1''' (03.05.2017; 1021515 Stellen, [https://www.primegrid.com/download/mega-3393389.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123342 Prime Pages])<br>
'''1049&sdot;2<sup>3395647</sup>+1''' (12.05.2017; 1022195 Stellen, [https://www.primegrid.com/download/mega-3395647.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123369 Prime Pages])<br>
'''611&sdot;2<sup>3398273</sup>+1''' (22.05.2017; 1022985 Stellen, [https://www.primegrid.com/download/mega-3398273.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123393 Prime Pages])<br>
'''1167&sdot;2<sup>3399748</sup>+1''' (27.05.2017; 1023430 Stellen, [https://www.primegrid.com/download/mega-3399748.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123402 Prime Pages])<br>
'''833&sdot;2<sup>3403765</sup>+1''' (13.06.2017; 1024639 Stellen, [https://www.primegrid.com/download/mega-3403765.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123522 Prime Pages])<br>
'''953&sdot;2<sup>3405729</sup>+1''' (20.06.2017; 1025230 Stellen, [https://www.primegrid.com/download/mega-3405729.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123570 Prime Pages])<br>
'''907&sdot;2<sup>3417890</sup>+1''' (05.08.2017; 1028891 Stellen, [https://www.primegrid.com/download/mega-3417890.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123812 Prime Pages])<br>
'''999&sdot;2<sup>3418885</sup>+1''' (09.08.2017; 1029190 Stellen, [https://www.primegrid.com/download/mega-3418885.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123830 Prime Pages])<br>
'''975&sdot;2<sup>3419230</sup>+1''' (10.08.2017; 1029294 Stellen, [https://www.primegrid.com/download/mega-3419230.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123834 Prime Pages])<br>
'''1005&sdot;2<sup>3420846</sup>+1''' (18.08.2017; 1029781 Stellen, [https://www.primegrid.com/download/mega-3420846.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123861 Prime Pages])<br>
'''1119&sdot;2<sup>3422189</sup>+1''' (24.08.2017; 1030185 Stellen, [https://www.primegrid.com/download/mega-3422189.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123864 Prime Pages])<br>
'''1127&sdot;2<sup>3427219</sup>+1''' (15.09.2017; 1031699 Stellen, [https://www.primegrid.com/download/mega-3427219.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123892 Prime Pages])<br>
'''911&sdot;2<sup>3432643</sup>+1''' (05.10.2017; 1033331 Stellen, [https://www.primegrid.com/download/mega-3432643.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123925 Prime Pages])<br>
'''1147&sdot;2<sup>3435970</sup>+1''' (17.10.2017; 1034334 Stellen, [https://www.primegrid.com/download/mega-3435970.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123953 Prime Pages])<br>
'''625&sdot;2<sup>3438572</sup>+1''' (27.10.2017; 1035117 Stellen, [https://www.primegrid.com/download/mega-3438572.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123964 Prime Pages])<br>
'''543&sdot;2<sup>3438810</sup>+1''' (29.10.2017; 1035188 Stellen, [https://www.primegrid.com/download/mega-3438810.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123973 Prime Pages])<br>
'''943&sdot;2<sup>3440196</sup>+1''' (02.11.2017; 1035606 Stellen, [https://www.primegrid.com/download/mega-3440196.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123980 Prime Pages])<br>
'''943&sdot;2<sup>3442990</sup>+1''' (13.11.2017; 1036447 Stellen, [https://www.primegrid.com/download/mega-3442990.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=123990 Prime Pages])<br>
'''1155&sdot;2<sup>3446253</sup>+1''' (27.11.2017; 1037429 Stellen, [https://www.primegrid.com/download/mega-3446253.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=124029 Prime Pages])<br>
'''1065&sdot;2<sup>3447906</sup>+1''' (03.12.2017; 1037927 Stellen, [https://www.primegrid.com/download/mega-3447906.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=124047 Prime Pages])<br>
'''1155&sdot;2<sup>3455254</sup>+1''' (28.12.2017; 1040139 Stellen, [https://www.primegrid.com/download/mega-3455254.pdf Bekanntgabe], [https://primes.utm.edu/primes/page.php?id=124096 Prime Pages])<br>
'''571&sdot;2<sup>3460216</sup>+1''' (20.01.2018; 1041632 Stellen, [https://primes.utm.edu/primes/page.php?id=124162 Prime Pages])