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1st 101-digit prime (Posted on 2018-08-02) Difficulty: 3 of 5
What is the smallest positive integer N that, when added to a googol (10^100), makes a prime number?

That number, a googol plus N, is called (UFINDIT).

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

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Solution computer solution | Comment 1 of 3
   10   point 80
   20   x=10^100
   30   y=fnNxprime(x)
   40   print y
   80   end
   90   '
10000   fnOddfact(N)
10010   local K=0,P
10030   while N@2=0
10040     N=N\2
10050     K=K+1
10060   wend
10070   P=pack(N,K)
10080   return(P)
10090   '
10100   fnPrime(N)
10110   local I,X,J,Y,Q,K,T,Ans
10120   if N@2=0 then Ans=0:goto *EndPrime
10125   O=fnOddfact(N-1)
10130   Q=member(O,1)
10140   K=member(O,2)
10150   I=0
10160   repeat
10170     repeat
10180       X=fnLrand(N)
10190     until X>1
10200     J=0
10210     Y=modpow(X,Q,N)
10220     loop
10230       if or{and{J=0,Y=1},Y=N-1} then goto *ProbPrime
10240       if and{J>0,Y=1} then goto *NotPrime
10250       J=J+1
10260       if J=K then goto *NotPrime
10270       Y=(Y*Y)@N
10280     endloop
10290    *ProbPrime
10300     I=I+1
10310   until I>50
10320   Ans=1
10330   goto *EndPrime
10340   *NotPrime
10350   Ans=0
10360   *EndPrime
10370   return(Ans)
10380   '
10400   fnLrand(N)
10410   local R
10415   N=int(N)
10420   R=(int(rnd*10^(alen(N)+2)))@N
10430   return(R)
10440   '
10500   fnNxprime(X)
10510   if X@2=0 then X=X+1
10520   while fnPrime(X)=0
10530     X=X+2
10540   wend
10550   return(X)
10560   '

finds the next prime after a googol to be a googol plus 267.

This agrees with OEIS's A049014:  n plus a googol is prime.  
267, 949, 1243, 1293, 1983, 2773, 2809, 2911, 2967, 3469, 3501, 3799, 4317, 4447, 4491, 5383, 5641, 5949, 6403, 6637, 6903, 7443, 8583, 8653, 9013, 9223, 9259, 9631, 10071, 10557, 10833, 10903, 11143, 11173, 11529, 11667, 11839, 12207, 12817

https://sites.google.com/site/pointlesslargenumberstuff/home/l/pgln2?tmpl=%2Fsystem%2Fapp%2Ftemplates%2Fprint%2F&showPrintDialog=1

shows this as being called Gooprol, but the site has mostly humorous newly coined words.

  Posted by Charlie on 2018-08-02 12:25:55
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