## Wall-Sun-Sun primes

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• 1) forprime (p=7,300,wss=p-quad5(p);print1(p : );for (n=1,wss,if (fibonacci(n)%p==0,print1(n , )));print()) forprime (p=7,500,wss=p-quad5(p);for (n=1,wss,if
Message 1 of 1 , Jan 4, 2003
1)

(fibonacci(n)%p==0,print1(n",")));print())

(n==wss,print1(p","),break))))
7,11,19,23,31,43,59,67,71,79,83,103,127,131,163,167,179,191,223,227,239,251,
271,283,311,359,367,379,383,419,431,439,443,463,467,479,487,491,499,
(n==wss,print1(n","),break))))
8,10,18,24,30,44,58,68,70,78,84,104,128,130,164,168,178,190,224,228,238,250,
270,284,310,358,368,378,384,418,430,438,444,464,468,478,488,490,498,
(n<wss,print1(p",");break))))
13,17,29,37,41,47,53,61,73,89,97,101,107,109,113,137,139,149,151,157,173,181
,193,197,199,211,229,233,241,257,263,269,277,281,293,307,313,317,331,337,347
,349,353,373,389,397,401,409,421,433,449,457,461,
(n<wss,print1(wss",");break))))
14,18,28,38,40,48,54,60,74,88,98,100,108,108,114,138,138,148,150,158,174,180
,194,198,198,210,228,234,240,258,264,268,278,280,294,308,314,318,330,338,348
,348,354,374,388,398,400,408,420,434,448,458,460,

Some code, determining which F{p-(p/5)} are the first Fn to be divisible by
p.

These look fairly evenly distributed. Is this so?

2)

I believe the solution to WSS primes, or lack of, lies in the Fibonacci
relation:

F(2k+1) = F(k+1)^2 + F(k)^2

Let either F(k+1) or F(k) be F(p), and use a mod3 and mod4 argument.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths/