News - January 2009

Jan 29, 2009

704^83-1: 828515320218807688050013637687.

776^83-1: 721938315218618813819300503411877.
776^83-1: 4398423367627633806509303296232316637641266075709489785533200494274166326712306728090328918918568562818137403.
Thus 776^83-1 should be completely factored.
          
904^83-1: 3235336204869160770921020233039.
9913^83-1: 73936347568144134937.
9913^83-1: 1520248236382064908571273.
9915^83-1: 8792387553252113.
9916^83-1: 2552977799497721915503.

9917^83-1: 167.
9917^83-1: 1163.
9917^83-1: 4969211993.
9917^83-1: 69442798826669308147.
9917^83-1: 75338774826556340361955688356555694415879828028077265598046940971951614391200283760983973305985971453942596435539365349456558922958455322990411825517662292609987195623898226591549108077545091327989684656001004216874258177644409291894018198501973779140505921476924357246827463099138735135201577.
Thus 9917^83-1 should be completely factored.

9923^83-1: 4649.
9923^83-1: 98529884653.
9923^83-1: 1680237838972039565677.
9923^83-1: 6172195907573951869931.
9923^83-1: 12267456277142947695931.
9923^83-1: 162160868242752896704163.
9923^83-1: 61434873128372942003085733.
9923^83-1: 9139354657734086044571456341110923182030763662835415984292418582109618715410695248039039980834175391966470939298823727229752911482394557895166587110261764203110702145002804886066909712874444268754523.
Thus 9923^83-1 should be completely factored.

I do not know if these factorizations are new.

Jan 23, 2009

2^9998+1: 142536232810849.
724^83-1: 496543299636806692426794857.
776^83-1: 7207071834543179106693811.
815^83-1: 4113214404761695456112951933.
904^83-1: 2065632631690422325997812326479.
3408^83-1: 1198522129247100855707.
9907^83-1: 342601210749422900813.

Jan 22, 2009

10^29510L+1: 17097321069865440821.

Jan 18, 2009

n=59060M: 37263631187121924301.
n=59180L: 139282249990404181.
n=59220M: 17731932332941.
n=59260L: 214599362917409441.
n=59420L: 32630645275883088641.
n=59580L: 74435245125841.
n=59580M: 345294228969181.
n=59860M: 12092382769921.
n=59860M: 1859449102802321.
n=59900M: 1592510361040540178201.
n=59980L: 7513433576456861.

Jan 16, 2009

335^88+1: 5645948387115668688190354541729.
335^88+1: 52313898208314544577107784129362697107766109337706897.

This factorization was started by the surprisingly existance of a C84 entry 
for Phi_(176,335) in What's new, history, errata (Hisanori Mishima). 
Msieve did it within a few minutes.

Jan 16, 2009

n=59020L: 47553013276803841.
n=59020M: 14765000278271101.
n=59060M: 158602580975645321.
n=59140L: 262574421291101.
n=59140L: 10237070419638751141.
n=59300M: 3967620747542701.
n=59700L: 21591068888931678001.
n=59740M: 291592212338807610335701.
n=59900M: 13614900776401.

Jan 14, 2009

n=59060M: 94241782726601.
n=59140M: 147797816105941.
n=59420L: 1167203267347682861.
n=59900M: 3379202074201.

Jan 13, 2009

n=24220M: 171319196206465721.
n=24538: 3323851054701557.
n=24802: 46283138764607.
n=24880: 6894809397246241.
n=24928: 14787790054529.
n=24968: 3302184220522221817.
n=25060M: 192612357015961.
n=25300L: 5063727018901.
n=25300L: 101307379102818901.
n=59740M: 15794175841061.

Jan 12, 2009

n=12805 : 299989576222938031.
n=19860L: 6371723569460365430245381.
This p25 was found with p-1 and bounds B1=1e6, B2=1e9.

n=37220M: 86597026208562601.
n=37420L: 2262812559000221.
n=37420M: 208099021140041.
n=38020M: 88382906785441.
n=38620L: 463819901772271741.
n=38780L: 440526874257121.
n=38980M: 67084914409421.
n=39660L: 42276234355417861.
n=41300M: 6929089248641347901.
n=41500L: 5653268651501.
n=41500M: 45095704752001.
n=41740L: 3962188199521.
n=44740M: 12844257973721.
n=86260M: 3286131804121.
n=86260M: 136700631869981.
n=86500L: 8405907207001.
n=86780M: 299854290129721.

Jan 7, 2009

n=25820M: 23613414214101221.
n=92300L: 183921065013401.
n=92660L: 40650361905932101.
n=93060M: 3183156106021.
n=93260M: 38723613978601.
n=93500L: 70154408742001.
n=93980L: 2586734244422744081.
n=94020L: 6931024276321.
n=94700L: 37664636806230901.
n=94740M: 1839681215401.

Jan 6, 2009

n=31620M: 95175181164783554241190501.
This p26 was found with p-1 and B1=1e6, B2=5e7.

n=49100L: 749497684787893801.
n=49140L: 782158040646091201.
n=49420L: 15089011241949401.
n=49660M: 11888215013221.

Jan 2, 2009

n=13900L: 37964253182561021441329901.

Jan 1, 2009

n=13220L: 920710003821937627768617447378781.
This p33 was found with p-1 and bounds B1=2e6, B2=9999974858-10320875692,
although the factorization of p33-1 is 
920710003821937627768617447378781-1 = 2^2.3.5.13^3.151.661.29339.43973.90227.601167131.

n=69260M: 1616251983341.
n=69460M: 656614088408581.
n=69620L: 25411760525648141.
n=69780M: 7877739272761.
n=69940L: 11141577302077301.
n=69940M: 292042788663601.
n=71380L: 2856323592581.
n=71740L: 762147825001.
n=71860L: 44194146788510561.
n=71940L: 3833782861339201.
n=71940M: 160920773975281.
n=73340L: 24242047092844847681.
n=73500L: 29796555138001.
n=73620L: 69770950298258761.
n=73780M: 3124685111521.
n=73940L: 3455040074921.
n=74140L: 72861961334801.
n=74300L: 4535713164523007801.
n=74420L: 1683302854361.
n=75460L: 1904597043581.
n=75540L: 3090368292241.
n=75540M: 450880508101.
n=75660M: 15430288112461.
n=77820M: 112250301089471709601.
n=77940M: 298254242312101.
n=81220M: 105564259355281.

Alfred Reich