Aimo Törn: Probabilistic Algorithms


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Finding large primes

The implemented Scheme function find-next-prime do not test numbers divisible by 2,5,7,11,13 and also makes some outputs so that its progress can be followed. The number of repetitions is set to 10.
>>> (find-next-prime (expt 10 200))
blank: number divisible by 3,5,7,11,13
f    : failed Fermat, F: passed Fermat
j    : failed Jakobi, J passed Jacobi

start:
1000...001
ff ff f      f f  ff    ff  f  f    ff
...
ff ff f  f   FFFFFFFFFFJJJJJJJJJJ
prime:
1000...357  (67f + 10F + 10J)

>>> (find-next-prime (expt 10 300))
...
start:
1000...001
...
prime
1000...331   (64f + 10F + 10J)
The computations above only took some minutes on a Macintosh PowerPC running an educational Scheme version.