Factorizations of Cyclotomic Numbers



Up to phi(n) <= 58 are completely factored.

phi(n)npublication
1 1, 2 not published
2 3, 4, 6
4 5, 8, 10, 12
6 7, 9, 14, 18
8 15, 16, 20, 24, 30
10 11, 22
12 13, 21, 26, 28, 36, 42
16 17, 32, 34, 40, 48, 60 Factorization of Cyclotomic Numbers
(Sophia Kokyuroku in Mathematics 26, November 1987)
18 19, 27, 38, 54
20 25, 33, 44, 50, 66 Factorization of Cyclotomic Numbers 2
(Sophia Kokyuroku in Mathematics 29, February 1989)
22 23, 46
24 35, 39, 45, 52, 56, 70, 72, 78, 84, 90 Factorization of Cyclotomic Numbers 3
(Sophia Kokyuroku in Mathematics 35, July 1992)
28 29, 58
30 31, 62 Factorization of Cyclotomic Numbers 4
(Sophia Kokyuroku in Mathematics 42, July 1999)
32 51, 64, 68, 80, 96, 102, 120
36 37, 57, 63, 74, 76, 108, 114, 126 (not published yet.)
40 41, 55, 75, 82, 88, 100, 110, 132, 150, (not published yet.)
42 43, 49, 86, 98 (not published yet.)
44 69, 92, 138 (not published yet.)
46 47, 94 (not published yet.)
48 65, 104, 105, 112, 130, 140, 144, 156, 168, 180, 210 (not published yet.)

Table 1
phi(n)nlast updatewho factored
36 37May 07, 2000Conrad Curry (last number)
57Feb. 14, 2001Aiichi Yamasaki, Sean A. Irvine (last number),
Tetsuya Kobayashi, Mark Belangee
63Feb. 17, 2001Aiichi Yamasaki, Yasunobu Torii, Sean A. Irvine (last number),
Tetsuya Kobayashi, Mark Belangee
74Oct. 04, 1999Aiichi Yamasaki (last number)
76Apr. 18, 1999Aiichi Yamasaki (last number)
108Aug. 04, 2000Yasunobu Torii (last number)
114Feb. 23, 2001Aiichi Yamasaki, Masaki Ukai, Hisanori Mishima,
Sean A. Irvine (last number)
126Feb. 07, 2001Aiichi Yamasaki, Masaki Ukai (last number),
Hisanori Mishima, Yasunobu Torii
40 41Oct. 25, 2000Tetsuya Izu (last number), Andy Steward
55Apr. 21, 2001Tetsuya Kobayashi, Jens Franke (last number)
75Jun. 23, 2001David A. Miller, Tetsuya Kobayashi, Satoshi Tomabechi, Yasunobu Torii,
Katsuyuki Okeya, Thorsten Kleinjung
82Apr. 24, 2001Satoshi Tomabechi, Tetsuya Kobayashi,
Katsuyuki Okeya (last number)
88Jan. 23, 2001Katsuyuki Okeya (last number), Sean Irvine
100May 10, 2001Satoshi Tomabechi, Tetsuya Kobayashi, Hisanori Mishima,
Jens Franke (last number)
110May 12, 2001David A. Miller, Jens Franke (last number)
132Jan. 13, 2002Tetsuya Izu, Sean Irvine, Joe Leherbauer (last number)
150Jun. 17, 2001Tetsuya Izu, Tetsuya Kobayashi, Yasunobu Torii,
Thorsten Kleinjung (last number)
42 43Jul. 01, 2001Andy Steward, Robert Backstrom (last number)
49Jan. 15, 2002Andy Steward, Satoshi Tomabechi, Kunihiko Miyazaki, Sean Irvine,
Henrik Olsen (last number), Carsten Pedersen (last number)
86Jul. 24, 2002Masaki Ukai, Tetsuya Kobayashi, Alexander Kruppa (last number)
98Apr. 03, 2002Masaki Ukai, Tetsuya Kobayashi, Alexander Kruppa (last number)
44 69Jan. 12, 2003Takahiro Nohara, Joe Leherbauer, Alexander Kruppa (last number)
92Nov. 02, 2002Tetsuya Kobayashi (last number), Jun Eto
138Apr. 27, 2003Tetsuya Kobayashi, David A. Miller, Sean A. Irvine (last number)
46 47Mar. 08, 2002Andy Steward, Satoshi Tomabechi, Henrik Olsen, Carsten Pedersen, Joe Leherbauer, Robert Backstrom (last number), Sean Irvine
94Aug. 13, 2003Tetsuya Kobayashi, Joe Leherbauer, Sean A. Irvine (last number), Robert G. Wilson v

Table 2
phi(n)nCunningham formlast updatewho's factoring
48 65x65- 1Feb. 09, 2005Aiichi Yamasaki, Masaki Ukai, Sean A. Irvine, Alexander Kruppa, Tetsuya Taniguchi, Tom Cage, Tetsuya Kobayashi (last number)
104x52+ 1Nov. 30, 2004Masaki Ukai, Steven Whitaker, Tomoya Adachi (last number)
105x105- 1Oct. 08, 2005Aiichi Yamasaki, Masaki Ukai, Souichi Murata, Tom Cage, Tetsuya Kobayashi (last number)
112x56+ 1Oct. 03, 2004Takahiro Nohara, Masaki Ukai, Tetsuya Kobayashi (last number)
130x65+ 1Feb. 26, 2005Masaki Ukai, Tetsuya Kobayashi (last number)
140x70+ 1Nov. 15, 2005Masaki Ukai, Aiichi Yamasaki, Tetsuya Kobayashi (last number), Tomoya Adachi, Tom Cage
144x72+ 1Oct. 12, 2004Masaki Ukai, Alexander Kruppa, Tetsuya Kobayashi (last number)
156x78+ 1Mar. 07, 2005Masaki Ukai, Aiichi Yamasaki, Tetsuya Kobayashi (last number)
168x84+ 1Dec. 25, 2004Masaki Ukai, Tetsuya Kobayashi (last number)
180x90+ 1Jan. 19, 2005Masaki Ukai, Aiichi Yamasaki, Philippe Strohl, Tomoya Adachi (last number)
210x105+ 1Mar. 23, 2005Takahiro Nohara, Masaki Ukai, Aiichi Yamasaki, Tetsuya Kobayashi (last number)
52 53x53- 1Jul. 01, 2006Masaki Ukai, Greg Childers, Andy Steward, Robert Backstrom, Hisanori Mishima, Alexander Kruppa (last number)
106x53+ 1Feb. 27, 2007Takahiro Nohara, Masaki Ukai, Hisanori Mishima, Greg Childers (last number)
54 81x81- 1Nov. 16, 2006Masaki Ukai, Sinkiti Sibata, Hisanori Mishima, Greg Childers (last number)
162x81+ 1Feb. 17, 2007Tetsuya Kobayashi, Masaki Ukai, Aiichi Yamasaki, Sinkiti Sibata, Hisanori Mishima, Tomoya Adachi (last number)
56 87x87- 1Jan 28, 2012Tetsuya Kobayashi, Aiichi Yamasaki, Greg Childers, Hisanori Mishima, Sander Hoogendoorn, Tim Morrow,
Masaki Ukai (last number)
116x58+ 1Mar. 21, 2012Tetsuya Kobayashi, Aiichi Yamasaki, Hisanori Mishima, Sander Hoogendoorn, Greg Childers,
Masaki Ukai (last number)
174x87+ 1Jun. 16, 2012Tetsuya Kobayashi, Aiichi Yamasaki, Hisanori Mishima, Sander Hoogendoorn,
Masaki Ukai (last number)
58 59x59- 1Nov. 28, 2011Takahiro Nohara, Sinkiti Sibata, Andy Steward, Robert Backstrom, Hisanori Mishima, Yeong Uk Jo, Kenji Ibusuki,
Masaki Ukai (last number)
118x59+ 1Sep. 19, 2008Masaki Ukai, Aiichi Yamasaki, Sinkiti Sibata, Hisanori Mishima,
Greg Childers (last number)


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E-mail : kc2h-msm@asahi-net.or.jp
Hisanori Mishima