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Old 2013-09-17, 21:25   #1
Batalov
 
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Mar 2008
Phi(4,2^7658614+1)/2

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Default The expected number of primes

Here's a couple of easy exercises:

1. How many primes does one expect to find in the class k*10^n-1, where 2<=k<=9 and 1000000<=n<1250000.
Hints for the small adjustments of probabilites:
a) k is in {2,3, 5,6, 8,9}
b) for k=8, remove n :: 3|n; for k=9, remove n :: 2|n
2. 10% of the range was checked and 1 prime was found. How many more primes does one expect to find?
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