News - April 2009

Apr 20, 2009
10^13090L+1: 104812264289041.
10^13250L+1: 225570962607009751001.
10^13310M+1: 554412917730482141.
10^13410M+1: 3576717318781.
10^19690M+1: 147751744002379701581.
10^19730M+1: 15622625940498200521.
10^19810L+1: 783498476659361.
10^19850M+1: 9104420135401.
10^19890M+1: 5347101021883444981. The remaining cofactor (4536 digits) is a probable prime.
10^19930M+1: 205456802425781.
10^19970L+1: 1107681601050781.
10^20008+1: 360054243311681.
10^20019+1: 10307863816609.
10^20033+1: 9265679707259.
10^20038+1: 26035489139489.
10^20043+1: 111741211469053.
10^20049+1: 3305593590967.
10^20054+1: 270235397764835941.
10^20097+1: 20465255498689.
10^20101+1: 214435070794943.
10^20129+1: 3103666556491.
10^20133+1: 247395790056997.
10^20145+1: 1726099951524211.
10^20146+1: 1086671024812129.
10^20146+1: 1169834458214129.
10^20148+1: 237312746576290081.
10^20177+1: 8243727301333.
10^20183+1: 69116437590329.
10^20184+1: 59947675873143338881.
10^20206+1: 11605122486109.
10^20219+1: 70259236022881.
10^20220+1: 444922058826001.
10^20247+1: 19812144907591213.
10^20248+1: 19235197105297.
10^20262+1: 5921928218449.
10^20284+1: 3405093984689.
10^20286+1: 21527202520909.
10^20287+1: 231354587631045121.
10^20291+1: 100432231748716771.
10^20339+1: 134817912835665379.
10^20357+1: 179619376347161.
10^20391+1: 20089740266569.
10^20399+1: 122946484435303.
10^20405+1: 618283389462971.
10^20422+1: 179842815420125401.
10^20441+1: 20578630193287.
10^20471+1: 2087156442026043407449.
10^20770L+1: 14204080634501.
10^21053+1: 338782103446219.
10^21070M+1: 99249960373621.
10^21070M+1: 3604519432807301.
10^21077+1: 4412868726841.
10^21110L+1: 408026306954221.
10^21130M+1: 3824588533354021.
10^21170L+1: 67679122560093041.
10^21190M+1: 7768915255141.
10^21270L+1: 1290308076033841.
10^21290M+1: 34797930340321.
10^21290M+1: 4480178830883916679121.
10^21330M+1: 22374223299214961467681.
10^21334+1: 38044022758561.
10^21350L+1: 9200160734411501.
10^21372+1: 5602626685816400137.
10^21466+1: 6335590549727909.
10^28030L+1: 129928882643701.
10^28070L+1: 60574600139075468041.
10^28070M+1: 40015206268575632965355521.
10^28210M+1: 46865756970761.
10^28230L+1: 161359140643932541.
10^28230L+1: 364930879450834561.
10^28290M+1: 3239555153590681.
10^28450L+1: 190568230305301.
10^28470L+1: 73199497119177001.
10^28510L+1: 5024985224183161.
10^28530L+1: 35804595376801.
10^28610M+1: 9855156181181.
10^28630M+1: 197145768931844260501.
10^28650L+1: 361264671585843102601.
10^28730M+1: 887142327970601.
10^28750L+1: 51414481303800001.
10^28810M+1: 2527961808374441.
10^28850M+1: 1400108878488601.
10^28870L+1: 215038720804979501.
10^28890L+1: 1404192551856601501.
10^28890M+1: 304254566108250841.

Apr 6, 2009
10^12730L+1: 18953810506026601.
10^12790L+1: 4791925658895729281.
10^12910M+1: 59982990911567100301.
10^19515+1: 304662312503011.
10^19554+1: 3173478299701.
10^19565+1: 10639890616811.
10^19580+1: 311649630796028801.
10^19599+1: 103775436552721.
10^19615+1: 1227503011438481.
10^19652+1: 127264214255441.
10^19962+1: 56323984912021.
10^19665+1: 27875330728291.
10^19667+1: 4521331394771.
10^19679+1: 5287343919859.
10^19684+1: 5020188463361.
10^19760+1: 142045721047361.
10^19772+1: 39762034571716697.
10^19882+1: 27105938803301.
10^19907+1: 8425006777729.
10^19911+1: 420251263976701081.
10^19920+1: 2168601567317761.
10^19966+1: 8146886668069.
10^20032+1: 610988939950849.
10^20037+1: 97644984849121.
10^20043+1: 490552344026281.
10^20115+1: 1132273764369001.
10^20195+1: 65741378687041.
10^20204+1: 6471204580553.
10^20213+1: 120872168560529.
10^20313+1: 6239312032411.
10^20388+1: 4340688383041.
10^20418+1: 20669811518761.
10^20426+1: 133733756650961209.
10^20436+1: 472123373011993.
10^20600+1: 10743438978401.
10^20853+1: 5310781357771.
10^21015+1: 56789487201858841.
10^21028+1: 4629933558713.
10^21037+1: 23349061733088281.
10^21083+1: 87830402798077.
10^21093+1: 5962219391503.
10^21114+1: 15237234641089.
10^21212+1: 139051893376849.
10^21252+1: 5023291120849.
10^21271+1: 3332173619956669357.
10^21273+1: 157492623205219.
10^21298+1: 2681319247788161.
10^21304+1: 9561009334993.
10^21318+1: 8847072880669.
10^21320+1: 16062362633880161.
10^21346+1: 23098649404741.
10^21362+1: 8723953481101.
10^21389+1: 104630286441133.
10^21400+1: 473206602484001.
10^21409+1: 49853367946973.
10^21438+1: 56833743491821.
10^21453+1: 84553163961037.
10^21460+1: 109029327523077601.
10^21494+1: 36612379219681.
10^25310L+1: 12211214814341.
10^26230L+1: 9467702342321.
10^28590M+1: 3800398254241.
10^28690L+1: 110747703098341.
10^30670M+1: 12476322846661.
10^32830L+1: 24814868435561.
10^43550M+1: 669791683601.

Any of these factors was found with p-1 (of course).

Factors for numbers of the form 100^n + 3·10^n + 43

Apr 23, 2009 (Kurt Beschorner)
n=74: 18772242202033409029877369.
n=78: 50002965033923197483051889208299.
n=79: 5629188280686288161095090679477024911.
n=81: 129059181210887893929642685111138169.
n=83: 128593175148914312081681670925189.
n=88: 9995065985695825325845317795009349553099.
n=91: 30158534424326963490256860356242757.

Apr 16, 2009 (Kurt Beschorner)
n=58: 1123341196747570583606925787517766169.