Let the minus-one-factorization of a prime P be the
factorization of P-1. Below are the minus-one-factorizations of the
prime moduli for the
Certicom Elliptic Curve Cryptography (ECC)
Challenges over prime fields, and the recursive
minus-one-factorizations of each large prime factor. If a number is
followed by a parenthesized expression, the parenthesized expression,
ignoring any parenthesized expressions within it, is the
minus-one-factorization of the number.
;; ECCp-131
1550031797834347859248576414813139942411 ( 2 5
155003179783434785924857641481313994241 ( 2 2 2 2 2 2 2 2 2 3 5
20182705700968071083965838734546093 ( 2 2 3 3 13 23 31 691 1063
35425647529 (2 2 2 3 1476068647 (2 3 13 13 211 6899)) 2324421561859 (
2 3 11 5591 6299143 (2 3 1049857 (2 2 2 2 2 2 2 2 3 1367))))))
;; ECCp-163
7441570001851253078325059510076520610606604922267 (2 3 19
281082065814119 (2 4021 34951761479 (2 9341 1870879 (2 3 79 3947)))
232234417559633389665439706088451 (2 3 5 5 199 601 1517753 (2 2 2 193
983) 42683677 (2 2 3 7 23 22093) 199822713017 (2 2 2 13709 1822003 (2
3 7 13 47 71) )))
;; ECCp-191
3088527565889291933677698411347346523477823907719021786597 (2 2 7
64817 176597 2831642591 (2 5 7 71 569747) 612429643268111 (2 5 61 3533
10831 26237) 5556822995668202328643 (2 3 11 13 13 37 13464623031049829
(2 2 11 11 11 17 181 821918311 (2 3 5 27397277 (2 2 1979 3461)))))
;; ECCp-239
862591559561497151050143615844796924047865589835498401307522524859467869
(2 2 79 97 683 32914695791553889 (2 2 2 2 2 3 13 26373954961181 (2 2 5
6481 11681 17419)) 1251802568002522287870807195430320302070461232107
(2 83 7949 17337811 (2 3 5 7 82561) 1865415619 (2 3 3 11 11 47 18223)
14584787891 (2 5 1458478789 (2 2 3 13 13 29 24799)) 2011153700906761
(2 2 2 3 5 16759614174223 (2 3 19 63607 2311289 (2 2 2 7 149 277)))) )
;; ECCp-359
815061317237192195822186322581994619328922585201839923945006339195983201432548797517008668016697623370770793
( 2 2 2 59 18761087 (2 29 323467) 32129831 (2 5 17 188999)
2864717788343148103646536857871784899879148861068940844995306009883386685231752208772094863
( 2 3 127 265921867653623936056279 ( 2 3 3 14773437091867996447571 (2
5 7 17 2477987 (2 7 263 673) 5009975039569 (2 2 2 2 3 104374479991 (2
3 5 11 3797 83299))) )
14137506615578070034728506896758540845078851196564075028357231269 ( 2
2 19 67 67 5414567 (2 2707283 (2 1353641 (2 2 2 5 43 787)))
677259217957139 (2 127 389 8951 765773) 1246739038251570197 (2 2 113
733 3762990734681 (2 2 2 5 226463 415409)) 9063906319214216867 (2 11
823 6301 79448081161 (2 2 2 3 5 7 61 1550509 (2 2 3 129209))))))