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