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April 28, 2020 2020 年 4 月 28 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=31489: c31489(1111111111......) = 1075970182610939077766201 * c31465(1032659760......)

# ECM B1=5e4, sigma=2795030700556035

n=31567: c31546(4089529604......) = 89467776154704014686769 * c31523(4570952559......)

# ECM B1=5e4, sigma=867681213623428

n=31601: c31601(1111111111......) = 8700549863923556796754027 * c31576(1277058494......)

# ECM B1=5e4, sigma=0:8761566935674878

# 201101 of 300000 Φn(10) factorization were cracked. 300000 個中 201101 個の Φn(10) の素因数が見つかりました。

# 18778 of 25997 Rprime factorization were cracked. 25997 個中 18778 個の Rprime の素因数が見つかりました。

April 24, 2020 2020 年 4 月 24 日 (Kurt Beschorner)

n=299927: x294210(5001214183......) = 141209565729862067 * c294193(3541696455......)

# ECM B1=11e3, sigma=6202532062032653

April 24, 2020 2020 年 4 月 24 日 (Alfred Eichhorn)

# via Kurt Beschorner

n=90187: c90187(1111111111......) = 5511973860992747650969729 * c90162(2015813461......)

# ECM B1=5e4, sigma=0:3080777569154888

# 201099 of 300000 Φn(10) factorization were cracked. 300000 個中 201099 個の Φn(10) の素因数が見つかりました。

# 18776 of 25997 Rprime factorization were cracked. 25997 個中 18776 個の Rprime の素因数が見つかりました。

April 24, 2020 2020 年 4 月 24 日 (-)

# CORRECTION

n=53447: c48373(4869450164......) is (probable) prime

# 1181 of 300000 Φn(10) factorization were finished. 300000 個中 1181 個の Φn(10) の素因数分解が終わりました。

$ ./pfgw64 -tc -q"(10^19-1)*(10^29-1)*(10^97-1)*(10^53447-1)/9/(10^551-1)/(10^1843-1)/(10^2813-1)/228179994373"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing (10^19-1)*(10^29-1)*(10^97-1)*(10^53447-1)/9/(10^551-1)/(10^1843-1)/(10^2813-1)/228179994373 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N-1 test using base 3
Running N-1 test using base 5
Running N-1 test using base 7
Running N+1 test using discriminant 13, base 2+sqrt(13)
(10^19-1)*(10^29-1)*(10^97-1)*(10^53447-1)/9/(10^551-1)/(10^1843-1)/(10^2813-1)/228179994373 is Fermat and Lucas PRP! (301.7003s+0.0037s)

April 23, 2020 2020 年 4 月 23 日 (-)

# CORRECTION

n=47483: c46913(7897562645......) is (probable) prime

n=48087: c29364(1930617237......) is (probable) prime

# 1180 of 300000 Φn(10) factorization were finished. 300000 個中 1180 個の Φn(10) の素因数分解が終わりました。

$ ./pfgw64 -tc -q"9*(10^47483-1)/(10^103-1)/(10^461-1)/11395921"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing 9*(10^47483-1)/(10^103-1)/(10^461-1)/11395921 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Running N+1 test using discriminant 11, base 1+sqrt(11)
9*(10^47483-1)/(10^103-1)/(10^461-1)/11395921 is Fermat and Lucas PRP! (179.2024s+0.0013s)
$ ./pfgw64 -tc -q"(10^27-1)*(10^117-1)*(10^1233-1)*(10^48087-1)/(10^9-1)/(10^351-1)/(10^3699-1)/(10^16029-1)/1346437/3846961"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing (10^27-1)*(10^117-1)*(10^1233-1)*(10^48087-1)/(10^9-1)/(10^351-1)/(10^3699-1)/(10^16029-1)/1346437/3846961 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Running N+1 test using discriminant 5, base 4+sqrt(5)
(10^27-1)*(10^117-1)*(10^1233-1)*(10^48087-1)/(10^9-1)/(10^351-1)/(10^3699-1)/(10^16029-1)/1346437/3846961 is Fermat and Lucas PRP! (70.3757s+0.0049s)

April 22, 2020 2020 年 4 月 22 日 (-)

# CORRECTION

n=44241: c29487(2545428322......) is (probable) prime

# 1178 of 300000 Φn(10) factorization were finished. 300000 個中 1178 個の Φn(10) の素因数分解が終わりました。

$ ./pfgw64 -tc -q"(10^44241-1)/(10^14747-1)/39286119"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing (10^44241-1)/(10^14747-1)/39286119 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
(10^44241-1)/(10^14747-1)/39286119 is Fermat and Lucas PRP! (78.7128s+0.0027s)

April 21, 2020 2020 年 4 月 21 日 (-)

# CORRECTION

n=38297: c32814(9791880029......) is (probable) prime

# 1177 of 300000 Φn(10) factorization were finished. 300000 個中 1177 個の Φn(10) の素因数分解が終わりました。

$ ./pfgw64 -tc -q"(10^38297-1)/(10^5471-1)/1021254342319"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing (10^38297-1)/(10^5471-1)/1021254342319 [N-1/N+1, Brillhart-Lehmer-Selfridge]

Running N-1 test using base 3
Running N-1 test using base 7
Running N+1 test using discriminant 17, base 1+sqrt(17)
(10^38297-1)/(10^5471-1)/1021254342319 is Fermat and Lucas PRP! (101.3083s+0.0022s)

April 20, 2020 2020 年 4 月 20 日 (-)

# CORRECTION

n=6881: c5840(2034958154......) is (probable) prime

# 1176 of 300000 Φn(10) factorization were finished. 300000 個中 1176 個の Φn(10) の素因数分解が終わりました。

$ ./pfgw64 -tc -q"(10^6881-1)/(10^983-1)/49141059632832877096172610809992897380296624365337454176129"
PFGW Version 3.8.3.64BIT.20161203.Win_Dev [GWNUM 28.6]

Primality testing (10^6881-1)/(10^983-1)/49141059632832877096172610809992897380296624365337454176129 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N+1 test using discriminant 13, base 1+sqrt(13)
(10^6881-1)/(10^983-1)/49141059632832877096172610809992897380296624365337454176129 is Fermat and Lucas PRP! (2.3361s+0.0007s)

April 16, 2020 2020 年 4 月 16 日 (Kurt Beschorner)

n=299912: c149952(9999000099......) = 4280532734261684449 * c149934(2335924222......)

# ECM B1=11e3, sigma=6007364260174254

Largest known factors that appear after the previous one
  1  n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017)
  2  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  3  n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020)
  4  n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013)
  5  n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016)
  6  n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017)
  7  n=2820M: 832530561417330269513686172453574642103980456844602894975421 (Eric_ch / Aug 23, 2016)
  8  n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018)
  9  n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011)
  10  n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018)
  11  n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018)
  12  n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015)
  13  n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017)
  14  n=199700M: 16745944922383579468094190800250901 (Serge Batalov / Jul 6, 2015)
  15  n=199900L: 612937240365283738637341628923301 (Serge Batalov / Jul 6, 2015)
  16  n=217319: 327136068049348903751880841 (Alfred Reich / Feb 18, 2019)
  17  n=299011: 221045463366486747587120747 (Alfred Reich / Feb 18, 2019)
  18  n=299807: 1096020580210100960507 (Alfred Reich / Feb 18, 2019)
  19  n=299912: 4280532734261684449 (Kurt Beschorner / Apr 16, 2020)
  20  n=299941: 476143900733778479 (Alfred Reich / Feb 18, 2019)
  21  n=299945: 5990837478401 (Makoto Kamada / Feb 18, 2019)
  22  n=299959: 5119084696133 (Makoto Kamada / Feb 18, 2019)
  23  n=299974: 4468934658761 (Makoto Kamada / Feb 18, 2019)
  24  n=299997: 4358711612449 (Makoto Kamada / Feb 18, 2019)
  25  n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019)

April 16, 2020 2020 年 4 月 16 日 (Danilo Nitsche)

# via Kurt Beschorner

n=299933: x299914(2500311553......) = 470768613790117 * c299899(5311126272......)

# mfaktc

April 15, 2020 2020 年 4 月 15 日 (Kurt Beschorner)

n=9029: c9008(8383505012......) = 1635319120734576358170774369706363 * c8975(5126525402......)

# ECM B1=1e6, sigma=0:8793739683518911

April 5, 2020 2020 年 4 月 5 日 (Yousuke Koide)

n=816: c242(3244696272......) = 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 * p125(1020907660......)

# SNFS

# 1175 of 300000 Φn(10) factorization were finished. 300000 個中 1175 個の Φn(10) の素因数分解が終わりました。

Largest known factors that appear after the previous one
  1  n=604: 188981422179250214477885038956646476812007525220846625175628245017547495717341304519447280552146559165713534073382085460954497219653965265520569 (NFS@Home / Mar 16, 2017)
  2  n=786: 22470645744200057762885095342697894721605325430609487291715500041029950763944163993319007373686738769124162721892380653 (Serge Batalov and Bruce Dodson / Aug 12, 2009)
  3  n=816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881 (Yousuke Koide / Apr 5, 2020)
  4  n=1540M: 647799461893729229242068652342456021003805852058736425973158141325454469108253161834095467738437014341 (NFS@Home / Sep 18, 2013)
  5  n=2340L: 54416219768345058780693800256182138078138198676424989328564702046179663087831396313663972761 (Bo Chen, Wenjie Fang, Maksym Voznyy and Kurt Beschorner / Feb 15, 2016)
  6  n=2700M: 71618803865606542412383896587352242997259054038820075447553395780556284501401142201 (Bo Chen, Maksym Voznyy, Wenjie Fang, Alfred Eichhorn and Kurt Beschorner / May 7, 2017)
  7  n=2820M: 832530561417330269513686172453574642103980456844602894975421 (Eric_ch / Aug 23, 2016)
  8  n=5900M: 593243597135622945022444401922545308692618865123732027101 (pi / Sep 17, 2018)
  9  n=13980M: 21166873440679239162423181074773929272724025103001 (Kurt Beschorner / Jul 14, 2011)
  10  n=103748: 1941549624124837091592820526305327246593529 (Makoto Kamada / Jun 18, 2018)
  11  n=112666: 356334694333381082120764457775238849699 (Makoto Kamada / Oct 17, 2018)
  12  n=120833: 79670409416595961896605938971188364397 (Maksym Voznyy / Nov 27, 2015)
  13  n=135070: 9855589830288396166509564150666175361 (Makoto Kamada / Dec 6, 2017)
  14  n=199700M: 16745944922383579468094190800250901 (Serge Batalov / Jul 6, 2015)
  15  n=199900L: 612937240365283738637341628923301 (Serge Batalov / Jul 6, 2015)
  16  n=217319: 327136068049348903751880841 (Alfred Reich / Feb 18, 2019)
  17  n=299011: 221045463366486747587120747 (Alfred Reich / Feb 18, 2019)
  18  n=299807: 1096020580210100960507 (Alfred Reich / Feb 18, 2019)
  19  n=299941: 476143900733778479 (Alfred Reich / Feb 18, 2019)
  20  n=299945: 5990837478401 (Makoto Kamada / Feb 18, 2019)
  21  n=299959: 5119084696133 (Makoto Kamada / Feb 18, 2019)
  22  n=299974: 4468934658761 (Makoto Kamada / Feb 18, 2019)
  23  n=299997: 4358711612449 (Makoto Kamada / Feb 18, 2019)
  24  n=300000: 47847600001 (Makoto Kamada / Feb 15, 2019)

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