According to Hardy and Wright (1979), the 44-digit Ferrier's prime

determined to be prime using only a mechanical calculator, is the largest prime found before the days of electronic computers. The Wolfram Language can verify primality of this number in a (small) fraction of a second, showing how far the art of numerical computation has advanced in the intervening years. It can be shown to be a probable prime almost instantaneously

  In[1]:= FerrierPrime = (2^148 + 1)/17;
  In[2]:= PrimeQ[FerrierPrime] // Timing
  Out[2]= {0.01 Second, True}

and verified to be an actual prime complete with primality certificate almost as quickly

  In[3]:= <<PrimalityProving`
  In[4]:= ProvablePrimeQ[FerrierPrime,
          "Certificate" -> True] // Timing
  Out[4]= {0.04 Second,{True,
    {20988936657440586486151264256610222593863921,17,
      {2,{3,2,{2}},{5,2,{2}},{7,3,{2,{3,2,{2}}}},
      {13,2,{2,{3,2,{2}}}},{19,
      2,{2,{3,2,{2}}}},{37,2,{2,{3,2,{2}}}},{73,5,{
        2,{3,2,{2}}}},{97,5,{2,{3,2,{2}}}},{109,
        6,{2,{3,2,{2}}}},{241,7,{2,{3,2,{2}},{5,2,{
        2}}}},{257,3,{2}},{433,5,{2,{3,2,{2}}}},{
        577,5,{2,{3,2,{2}}}},{673,5,{2,{3,2,{2}},{
        7,3,{2,{3,2,{2}}}}}},{38737,5,{2,{3,2,{2}},
        {269,2,{2,{67,2,{2,{3,2,{2}},{11,2,{2,{5,
        2,{2}}}}}}}}}},{487824887233,5,{2,{3,2,{2}},{
        1091,2,{2,{5,2,{2}},{109,6,{2,{3,2,{2}}}}}},
        {28751,14,{2,{5,2,{2}},{23,5,
        {2,{11,2,{2,{5,2,{2}}}}}}}}}}}}}}

REFERENCES:

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 16-22, 1979.