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Monstrous prime? (Posted on 2012-10-29) Difficulty: 3 of 5
Given a number N=117355392^3+262963008^3+107575776^3 state if it is a prime number or not.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 2.6667 (3 votes)

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Some Thoughts re(2): Prime? Comment 3 of 3 |
(In reply to re: Prime? by Danish Ahmed Khan)

While the problem doesn't ask for the factorization, now that your comment does:

    5     Num=117355392^3+262963008^3+107575776^3:print Num
   10     S$="":N=abs(Num)
   20     if N>0 then Limit=sqrt(N):else Limit=0
   30     if Limit<>int(Limit) then Limit=int(Limit+1)
   40     Dv=2:gosub *DivideIt
   50     Dv=3:gosub *DivideIt
   60     Dv=5:gosub *DivideIt
   70     Dv=7
   80     loop
   90      if Dv>Limit then goto *Afterloop
  100      gosub *DivideIt:Dv=Dv+4 '11
  110      gosub *DivideIt:Dv=Dv+2 '13
  120      gosub *DivideIt:Dv=Dv+4 '17
  130      gosub *DivideIt:Dv=Dv+2 '19
  140      gosub *DivideIt:Dv=Dv+4 '23
  150      gosub *DivideIt:Dv=Dv+6 '29
  160      gosub *DivideIt:Dv=Dv+2 '31
  170      gosub *DivideIt:Dv=Dv+6 '37
  180      if inkey=chr(27) then S$=chr(27):end
  190    endloop
  200    *Afterloop
  210    if N>1 then S$=S$+str(N)
  220    print S$
  230   end
  240
  250   *DivideIt
  260    loop
  270     Q=int(N/Dv)
  280     if Q*Dv=N and N>0 then
  290       :N=Q:S$=S$+str(Dv)
  300       :if N>0 then Limit=sqrt(N):else Limit=0:endif
  310       :if Limit<>int(Limit) then Limit=int(Limit+1):endif
  320      :else
  330      :goto *Afterdo
  340     :endif
  350    endloop
  360    *Afterdo
  370    return
OK
run
 21044950027780650238181376
 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 7 7 7 7 7 7 7 7 7 11 11 11 4049 4051

meaning that N =  21044950027780650238181376, and the factorization is the listed primes, or more concisely:

2^15 * 3^6 * 7^9 * 11^3 * 4049 * 4051


  Posted by Charlie on 2012-10-30 17:06:29
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