[numerology] yet more primes

Don Reble djr at nk.ca
Tue Dec 16 14:06:18 CET 2003

Others have sought prime lists, wherein one must always add the offset.
(So there's no difference between population and depth.) There are two
kinds of particular interest.

1) Cunningham chains:
The multiplier is two, and the offset is either +1 or -1.
So far, they've found:
    2n-1, starting at 69257563144280941; length is 15 (see A005603, A064812)
    2n+1, starting at 95405042230542329; length is 14 (see A005602)
When converted to trees (offset +-1), those starting points yield no new
primes; but they're still deeper than (50n+-27, from 1879).

2) Arithmetic sequences of primes
Here the multiplier is one. A record-holder is
    1n+4609098694200, starting at 11410337850553; length is 22
    (see http://mathworld.wolfram.com/PrimeArithmeticProgression.html )
But it's silly to make a tree with a multiplier of one.

Don Reble       djr at nk.ca

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