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Getting Primed With Subtraction And Addition (Posted on 2007-12-26) Difficulty: 2 of 5
Determine all possible primes p such that each of p-8, p-4, p+8 and p+12 are also primes.

See The Solution Submitted by K Sengupta    
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Some Thoughts computer exploration (spoiler) | Comment 1 of 5

The P in the following program is 8 lower than the p of the puzzle, and tests P+4, P+8 (the original p of the puzzle), P+16 and P+20 for primality, and finds only P=3 (puzzle's original p=11) when testing all P through 131,708,999, at which point it was manually interrupted.

list
   10   loop
   15    Pp=P
   20    P=nxtprm(P)
   30    if prmdiv(P+4)=P+4 then
   40      :if prmdiv(P+8)=P+8 then
   50          :if prmdiv(P+16)=P+16 then
   60              :if prmdiv(P+20)=P+20 then
   70                  :print P;P+4;P+8;P+16;P+20
   75   if P=0 then goto 100
   80   endloop
  100   print Pp
OK
asave "5primes"
OK
run
 3  7  11  19  23
Break in 20
?p,pp
 131709001       131708999
OK

  Posted by Charlie on 2007-12-26 11:59:39
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