{-
Known factors of small Fermat numbers, transcribed from
http://www.prothsearch.com/fermat.html

This code is public domain.
-}
module Fermatfactors(initfactors,getprimefactor,K(K),N(N),Fermatrecord) where {

type Ii = Integer;

newtype K = K Ii deriving Show;
newtype N = N Ii deriving Show;
type Fermatrecord = (K,N);

getprimefactor :: Fermatrecord -> Ii;
getprimefactor (K k , N n ) = (k * 2^n) + 1;

-- http://www.prothsearch.com/fermat.html
-- as of 2020-12-01

-- all but the largest factor.
-- the remaining largest factor may be prime or composite.
initfactors :: [(Ii,[Fermatrecord])];
initfactors =
[ ( 0, [])
, ( 1, [])
, ( 2, [])
, ( 3, [])
, ( 4, [])
, ( 5, [(K 5, N 7)])
, ( 6, [(K 1071, N 8)])
, ( 7, [(K 116503103764643, N 9)])
, ( 8, [(K 604944512477, N 11)])
, ( 9, [(K 37, N 16)
       ,(K 3640431067210880961102244011816628378312190597, N 11)])
, (10, [(K 11131, N 12)
       ,(K 395937, N 14)
       ,(K 1137640572563481089664199400165229051, N 12)])
, (11, [(K 39, N 13)
       ,(K 119, N 13)
       ,(K 10253207784531279, N 14)
       ,(K 434673084282938711, N 13)])
, (12, [(K 7, N 14)
       ,(K 397, N 16)
       ,(K 973, N 16)
       ,(K 11613415, N 14)
       ,(K 76668221077, N 14)
       ,(K 17353230210429594579133099699123162989482444520899, N 15)])
, (13, [(K 41365885, N 16)
       ,(K 20323554055421, N 17)
       ,(K 6872386635861, N 19)
       ,(K 609485665932753836099, N 19)])
, (14, [(K 1784180997819127957596374417642156545110881094717, N 16)])
, (15, [(K 579, N 21)
       ,(K 17753925353, N 17)
       ,(K 1287603889690528658928101555, N 17)])
, (16, [(K 1575, N 19)
       ,(K 180227048850079840107, N 20)])
, (17, [(K 59251857, N 19)
       ,(K 14783975791554494074552473179612897725474511, N 19)])
, (18, [(K 13, N 20)
       ,(K 9688698137266697, N 23)])
, (19, [(K 33629, N 21)
       ,(K 308385, N 21)
       ,(K 8962167624028624126082526703, N 22)])
, (20, [])
, (21, [(K 534689, N 23)])
, (22, [(K 3853959202444067657533632211, N 24)])
, (23, [(K 5, N 25)])
, (24, [])
, (25, [(K 48413, N 29)
       ,(K 1522849979, N 27)
       ,(K 16168301139, N 27)])
, (26, [(K 143165, N 29)])
-- currently largest known Mersenne prime would be around here
, (27, [(K 141015, N 30)
       ,(K 430816215, N 29)])
, (28, [(K 25709319373, N 36)])
, (29, [(K 1120049, N 31)])
, (30, [(K 149041, N 32)
       ,(K 127589, N 33)])
, (31, [(K 5463561471303, N 33)])
, (32, [(K 1479, N 34)])
, (33, [])
, (34, [])
, (35, [])
, (36, [(K 5, N 39)
       ,(K 3759613, N 38)])
, (37, [(K 1275438465, N 39)])
-- GMP maximum 2^37 bits
, (38, [(K 3, N 41)
       ,(K 2653, N 40)])
, (39, [(K 21, N 41)
       ,(K 2864929972774011, N 41)])
, (40, [])
, (41, [])
, (42, [(K 43485, N 45)
       ,(K 111318179143061, N 45)])
, (43, [(K 212675402445, N 45)])
, (44, [])
, (45, [])
, (46, [])
, (47, [])
, (48, [(K 2139543641769, N 50)])
, (49, [])
, (50, [])
, (51, [])
, (52, [(K 4119, N 54)
       ,(K 21626655, N 54)
       ,(K 81909357657279, N 54)])
, (53, [])
, (54, [])
, (55, [(K 29, N 57)])
, (56, [])
, (57, [])
, (58, [(K 95, N 61)])
, (59, [])
, (60, [])
, (61, [(K 54985063, N 66)])
, (62, [(K 697, N 64)])
, (63, [(K 9, N 67)])
, (64, [(K 17853639, N 67)])
];

} --end