October 1st 2005

Admissible Prime Sets

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3. Counter-example

Finding a counter-example for the second Hardy-Littlewood conjecture, i.e. the prime counting function is not convex, is more or less impossible. However, I did some estimates and calculations related to this issue:
The only set for m = 46 which has 54 primes is
560651168351945542265568623882043856206800351003857634040218867197345773820708901 + Set 4
The only set for m = 47 which starts with 7 primes is a subset of Set 11
677039857508525000692405150755887372006330981606535979970170582458895880942908768091 + {0, 6, 8, 20, 30, 32, 36}
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