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Long chain (Posted on 2015-04-10) Difficulty: 3 of 5
Create a chain of consecutive digits starting with 1 and following 9 by 0: 123456789012345...

How many digits are needed to obtain the 1st prime number?

See The Solution Submitted by Ady TZIDON    
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Some Thoughts computer exploration | Comment 1 of 7
Well, the 1st prime number is 2, and you have one right there as the second digit.

If you mean When will the entire string of digits first represent a prime number, I doubt that it ever will. The program below gets to a length of over 1000 digits without finding a prime. (It stops with an overflow in line 40).

   10   S=""
   20   while Found=0
   30    for I=1 to 10
   40       S=S+cutspc(str(I @ 10))
   50       V=val(S)
   60       P=prmdiv(V)
   70       if p>1 then if P=V  or fnPrime(v) then print V:Found=1
   80    next
   90   wend
  999   end 
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   '

  Posted by Charlie on 2015-04-10 20:46:20
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