The following program finds repunits with 2, 19 and 23 digits are prime. It was stopped at a number of digits of 188. No other repunit primes were found; the other repunits checked were definitely not prime; the ones identified as prime were "probably" prime to a high degree of certainty. Thus they were checked via Wolfram Alpha to assure they are indeed prime.

   10   Repu=1

   20   for Ndig=2 to 333

   30      Repu=10*Repu+1

   40      if fnPrime(Repu) then print Ndig,Repu

   50   next

  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   '