At a better time, this would be or would have been a good (relative) time to advance a statistical partial definition of how much of a coincidence this is among a certain class of sequences (while advancing my knowledge of statistics).

At present, I would be over-Solomonizing my own mind, however, to attempt that (if you can see what that means locally).

Such would be unwise (but I'd like to consider you my oldest cousin, with no desired disregard for my immediate family (It seems like it seams right, because of one A.L., and not addressing this specifically leaves another A.L. still)).

James

--- On Fri, 5/17/13, Jens Kruse Andersen <jens.k.a@...> wrote:

From: Jens Kruse Andersen <jens.k.a@...>

Subject: Re: [PrimeNumbers] Check guess, please (simultaneous primes in sequence)

To: primenumbers@yahoogroups.com

Date: Friday, May 17, 2013, 6:45 PM

James Merickel wrote:

> I don't have the first 15 terms with me, but THEY are easy

> [The first collection of] 8 simultaneous primes are to be found

> by adding/subtracting 1, 2, 4 and 5 to a (the sequence's) value,

> multiplying by a power of 10 and adding 1.

(827942544791 +/- n)*10^16+1 is prime for n = 1, 2, 4, 5

827942544791 is the first solution. It did come later than expected.

This seems like a coincidence. The next solutions are:

1028465717858, 1086965448791, 1562679711122, 1609404153257, 1800846280763

> {I also happen to have submitted to 'Prime Curios!' the value for

> 12 simultaneous and the power is 1 (where 8 and 10 are added to

> the list. ... A next step would be adding/subtracting 13.}

(9477895607701082 +/- n)*10+1 is prime for n = 1, 2, 4, 5, 8, 10, 13

This is the smallest solution. It also gives primes for n = 17.

--

Jens Kruse Andersen

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