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 Primed Palindromes (Posted on 2008-12-27)
A prime number less than 100 is increased by 1 and squared.
This square is incremented by 1 to yield a prime which is then squared.
The digits of this second square are reversed and added to that square resulting in a palindrome.

For which primes does this occur?

 See The Solution Submitted by brianjn No Rating

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 computer solution Comment 2 of 2 |

The primes are 19 and 89:

`  n (n+1)^2  (n+1)^2+1    ((n+1)^2+1)^2  palindromic             also prime                      sum 19    400        401          160801      268862 89   8100       8101        65626201    75888857`
`   10   while N<100   20    N=nxtprm(N)   30    Sq=(N+1)^2   40    Pr=Sq+1   50    if prmdiv(Pr)=Pr then   60      :Prsq=Pr*Pr:P2=Prsq   70      :Revd=0   80      :while P2>0   90        :Revd=10*Revd+P2@10:P2=P2\10  100      :wend  110      :Pal=Prsq+Revd  120      :S=cutspc(str(Pal))  130      :Good=1  140      :for I=1 to int(len(S)/2)  150        :if mid(S,I,1)<>mid(S,len(S)+1-I,1) then Good=0:endif  160      :next I  170      :if Good then print N;Sq;Pr;Prsq;Pal  180   wend`

 Posted by Charlie on 2008-12-27 23:47:41

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