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A prime and a cube (Posted on 2020-07-13) Difficulty: 2 of 5
What prime numbers p exist such that 16p+1 is a perfect cube?

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (3 votes)

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re: Just an observation | Comment 2 of 11 |
(In reply to Just an observation by Charlie)

I stopped that program at p=1384433 without having found another answer.  I'll try another tack: Take cubes and subtract 1 and divide by 16; if the answer is an integer, I'll check for primality.


   10   for Cr=2 to 1000000000
   20      C=Cr*Cr*Cr
   30      P=(C-1)/16
   40      if P=int(P) then P=int(P)
   41         :print P
   42                 :if prmdiv(P)=P then print P,C,Cr::stop:endif
   50                 :if prmdiv(P)=0 then cancel for:goto 100
   60   next
  100   end

It's quickly getting to 16 digit values of p and then some, without finding any more primes. The values found in the preceding post are the only ones found.

  Posted by Charlie on 2020-07-13 15:44:09
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