News - December 2010
December 19, 2010
10^23690M+1: 13055005269941.
10^24810M+1: 94211350366381.
10^31150M+1: 74420208074801.
10^48010L+1: 15834972089381.
10^14270L+1: 329464206767581.
10^25290L+1: 682752399708781.
10^44730M+1: 423850319596621.
423850319596621 - 1 = 2^2 · 3^11 · 5 · 7^2 · 71 · 137 · 251
10^12530M+1: 1304941222619161.
10^19230M+1: 6386199901785601.
10^26710L+1: 3533393677655761.
10^32530M+1: 5691262037332681.
10^33070L+1: 3259802171715581.
10^33310M+1: 1304661412412741.
10^35070M+1: 9186799271513641.
10^35390M+1: 1375203821623081.
10^12950L+1: 13704618377807701.
10^17510L+1: 34735132429846201.
10^26950L+1: 94859796036135901.
10^32890L+1: 16646138387361341.
10^37770L+1: 98276218336825381.
10^38390L+1: 18633578554263641.
10^41150M+1: 36180129507952901.
10^41710M+1: 40829912182583921.
10^48270L+1: 16304172726130501.
10^17070M+1: 704609659465764121.
10^23670M+1: 113163714435027961.
10^23830M+1: 159754725756938581.
10^25210M+1: 149485916587362181.
10^27550M+1: 675078533730687601.
10^29110M+1: 807749610900210761.
10^38370M+1: 374248578463840141.
10^40810L+1: 165892225183326181.
10^48450L+1: 170101606910205301.
10^16750L+1: 8438452815784435501.
10^22670L+1: 4363691029782646241.
10^23390L+1: 1522924039734213461.
10^25270L+1: 3764244590169412861.
10^30350L+1: 6374432607943917301.
10^30990L+1: 3804767165691055321.
10^31550M+1: 2264167294052821301.
10^33150L+1: 1054402420742704801.
10^36110L+1: 9020135104369957241.
10^41310M+1: 1784763975164554081.
10^42470L+1: 2978377392702548381.
10^43530M+1: 6686537838202932781.
10^46470L+1: 8579511591223852861.
10^47690L+1: 1303206075879300401.
10^18610M+1: 35292813744923405401.
10^23010M+1: 24182504416909957561.
10^23570L+1: 79115520710173344161.
10^25210M+1: 14764244014807000981.
10^25930M+1: 83539504647377758961.
10^27650M+1: 10299571977767073401.
10^27950M+1: 41524300973994521801.
10^28930L+1: 83605392613344430181.
10^30350M+1: 10155715445707909001.
10^30390M+1: 11420120134223014561.
10^36910L+1: 10397782857535521641.
10^38050L+1: 20534853418363588001.
10^42570M+1: 94359332468502246421.
10^12850M+1: 125171379263069055701.
10^17010M+1: 441527209812818555581.
10^20350M+1: 417611173194342975101.
10^20950L+1: 631159667782425895601.
10^24870M+1: 426892581836355937201.
10^33030L+1: 832454043670527204061.
10^35390L+1: 387793369327658428441.
10^43730M+1: 310622262335569454041.
10^47670M+1: 398029959411773084761.
10^48490M+1: 101267813344629677201.
10^49870L+1: 456531863767106326181.
10^22070M+1: 8980406800328625305201.
10^24750L+1: 2940127486878232084501.
10^48190L+1: 1082493988508258450461.
10^19050L+1: 50381952288958440708601.
10^22630L+1: 11743072637467785826441.
10^23910M+1: 98114893375565447114821.
10^35530M+1: 21549295254455511361061.
10^41230M+1: 29918578086001502002561.
10^17710M+1: 193821575772659280082561.
10^17890M+1: 100011353647048185642241. Found by Serge Batalov, Dec 6, 2010.
10^23530M+1: 450545439664397979873401.
10^25210M+1: 112392146316700149121441.
10^31550L+1: 823120996920652066620701.
10^37010L+1: 100214315714092674846901.
10^42270L+1: 838488617833083291536881.
10^43610L+1: 167978201494503938156501.
10^45510L+1: 141609462075024248534461.
10^16850L+1: 5377348809663968671750901.
10^19010M+1: 2996357917115559088428841.
10^23510M+1: 2233815069879680610750221.
10^24490L+1: 8012599465594530238516801.
10^24930L+1: 2028384706347983239158421.
10^31030L+1: 1050439010735195506303181.
10^31730L+1: 7891755910260035637222901.
10^32670M+1: 1270390880786166425680021.
10^35770M+1: 1657544388036128561893981.
10^43390L+1: 2366185604116388593431601.
10^45950L+1: 8243956737890053517838101.
10^48790M+1: 1096310621292742766480641.
10^14730L+1: 61231252869973723408615801.
10^25110L+1: 39014404102351617687874801.
10^45690M+1: 52251738682921546390614961.
10^46530M+1: 70072989603434840580200281.
10^35170M+1: 315496064767146102025399861.
10^30810M+1: 2092097946229230799357926481. Found by Serge Batalov, Dec 6, 2010.
10^47770L+1: 1514042552200872299475805301.
10^36790L+1: 37342417495061621511265951801.
10^16730M+1: 143073612933960977378098121701.
10^24390L+1: 129711324072293286777808231321.
10^40270L+1: 115292375845557608175544049341.
10^49610L+1: 30847430620382008736997413844941.
10^31131-1: 337801817473867. Found by Serge Batalov, Dec 11, 2010.
December 12, 2010
Factoring 100^84+3·10^3+109, GMP-ECM reported a factorization of type c121 = c63·p59.
Input number is 5404880983494420534015652209433328750098873586836951102170035157813076697459910614903486059233453543787072267304277430921 (121 digits)
Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=3892625261
Step 1 took 639ms
Step 2 took 624ms
********** Factor found in step 2: 131230201159606114933009304947389133728922081241742397482837907
Found composite factor of 63 digits: 131230201159606114933009304947389133728922081241742397482837907
Probable prime cofactor 41186258465921589433846432244058027626191935168570255439603 has 59 digits
December 12, 2010 (P-1)
10^41350L+1: 7732652742988151960568776872507813340801.
Resuming P-1 residue saved by AR@AR-PC with GMP-ECM 6.2.3 on Sat Dec 11 17:16:37 2010
Input number is 1144007532...8031435801 (16512 digits)
Using B1=300000-400000, B2=299973638-620874472, polynomial x^1
Step 1 took 97188ms
Step 2 took 56941ms
********** Factor found in step 2: 7732652742988151960568776872507813340801
Found probable prime factor of 40 digits: 7732652742988151960568776872507813340801
Composite cofactor 1479450288..(snipped)..9242095001 has 16472 digits
P-1 was successful because of 7732652742988151960568776872507813340801 − 1 = 2^7 · 5^2 · 7 · 41 · 383 · 827 · 1447 · 2909 · 3373 · 32713 · 159763 · 358234307.
p40 = 7732652742988151960568776872507813340801 is the largest factor of any Phi(n,10) in the range n = 13021..100000, compare Makoto Kamada's list Phin10.txt.
Alfred Reich