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By 1588 Pietro Cataldi had correctly verified that 217-1 = 131071
and 219-1 = 524287 are both prime.
But Cataldi also had incorrectly stated 2n-1 was also prime
for each of 23, 29, 31 and 37. This is interesting because Cataldi made his discoveries
by constructing what Shanks calls "the first extensive table of primes--up
to 750". These tables are big enough to show 219-1 is prime (its
square root is approximately 724) but not large enough to handle these
four larger numbers!
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