But is it, really?
That was already the era of "information overload" and "future shock."
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Rule of thumb: Want a 1024-bit prime? Try 1024 1024-bit candidates and you'll probably find one. Want a 4096-bit prime? Try 4096 4096-bit candidates and you'll probably find one.
The approximate spacing of primes around p is ln(p), so ln(2^1024) = 1024*ln(2), and ln(2)=0.693 so if you are willing to absorb 0.693 into your rule of thumb as a safety margin you get the delightfully simple rule of thumb above. Of course, you'll still want to use a sieve to quickly reject numbers divisible by 2, 3, 5, 7, etc, and this easily rejects 90% of numbers, and then do a Fermat primality test on the remainders (which if you squint is sort of like "try RSA, see if it works"), and then do Miller-Rabin test to really smash down the probability that your candidate isn't prime. The probabilities can be made absurdly small, but it still feels a bit scandalous that the whole thing is probabilistic.
EDIT: updated rule of thumb to reflect random candidate choice rather than sequential candidate choice.
Also interesting to note that not only has Berulis' attorney lead multiple lawsuits against the Trump administration in the past, he was also an intern for both Chuck Schumer and Hillary Clinton. Now that obviously doesn't prove anything, but it could nonetheless be considered a strong indicator this all might be politically-motivated.