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Interesting Sequence (3) (Posted on 2004-10-04) Difficulty: 1 of 5
What year comes next in the following sequence?

1973 1979 1987 1993 1997 1999

See The Solution Submitted by SilverKnight    
Rating: 2.4000 (5 votes)

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re: Any Easier way ? | Comment 4 of 9 |
(In reply to Any Easier way ? by Syzygy)

UBASIC has a nxtprm function to find the next prime after a given number, and it's used in:

10 n=1972
20 for i = 1 to 8
30       n=nxtprm(n)
40       ? n
50 next

which finds

run
 1973
 1979
 1987
 1993
 1997
 1999
 2003
 2011
OK

The nxtprm function in UBASIC doesn't work beyond 2^32=4,294,967,296.  A probabilistic primality test, derived from Donald Knuth's The Art of Computer Programming, is incorporated in this following program which finds the next prime after one googol:

   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   '

BTW it finds 10^100+267.


  Posted by Charlie on 2004-10-04 11:33:50
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