18.5 The period length of a prime 525
Appendix: Primitive prime divisors of repunits
n 211 Primitive prime divisors of. Rn(^33) 4 101, (^37) ..
(^54167) ,, 13271 ..
7 239 873 ,, 1374649 ..
10 90919 333667..
11 2164912 9901., 513239.
13 5314 909091, 79 , (^265371653)..
15 3116 17,, 29061615882353 ..
17 207172318 19, 52579 ,. 5363222357.
19 111111111111111111120 3541, 27961..
22 2321 43,,^19334093 ,,^108386898779..
23 1111111111111111111111124 99990001..
25 2140126 859, 1058313049 , 25601 , (^182521213001)..
27 75728 29,, 281440334654777631 , 121499449..
29 319130 211, 241 , (^16763) , 2161 , (^43037). , 62003 , 77843839397.
31 279132 353, 449 , (^6943319) , 641 ,, 140957336415063790604359 , 69857..
33 6734 103,, (^13446282103132983734013) , 21993833369 ..
35 7136 999999000001, 123551 , (^102598800232111471)..
37 202811938 909090909090909091, 247629013 ,. 2212394296770203368013.
39 90090090090099099099099140 1676321, 5964848081..
41 8342 127,, 12312689 ,, 538987459691 ,. 201763709900322803748657942361.
43 17344 89,, 10527889691527791 , (^1963506722254397) , 1056689261. , 2140992015395526641.
45 23868146 47, 139 ,, (^41855028301331107212531) , 549797184491917 ..
47 3512140948 9999999900000001, (^316362908763458525001406154038726382279)..
49 50588599750 251, 5051 ,, 788759434722011976730144598190963568023014679333..
Exercise
Find all prime numberspfor which^1 phas period length 11.^9
(^9) Problem 2207,J. Recreational Math., 27 (1995) 59.