I tried for P1=7, got to n=7350 with no result, and pulled the plug.

]]>Backwards check (in M), where e1 and e2 are the two absolute +/- Ps elements:

Input: a = FactorInteger[(e1 + e2)/2]; {First[First[a]], Length[a]}

Output: {61001,154}

My code looks a bit clunky with the repeat "First[First", but it works and I don't know how to improve it.

Prime factor range is 61001 to 62761, which comprises 154 primes. 61001 and 62761 are the 6146th and 6299th primes (respectively), but I don't know how that information can be used.

]]>For P1<=p_10000 there is nothing for 34<=n<=54 and 58<=n<=68.

Also did a search for (P1,n) pairs where P1 can go up to p_100000 and 34<=n<=68.

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P1 is the first prime in the sequence, and n is the number of primes in the sequence.

P1=2, n=4

2+3+5+7=17

2*3*5*7=210

210-17=193

210+17=227

Ps={193,227}

P1=3,n=2

3+5=8

3*5=15

15-8=7

15+8=23

Ps={7,23}

Let P1=2 and n=4

Ps={193, 227}

How are you getting this? It seems I have misread something...

]]>For P1=5 and n < = 1000 other than n = 2 and n = 6, I can find no others.

For P1=7 and n < = 1000, I can find no solutions.

For P1=11 and n < = 1000, I can find no solutions.

For P1=13 and n < = 1000 other than n = 2, I can find no others.

For P1=17 and n < = 1000, I can find no solutions.

For P1=19 and n < = 1000, I can find no solutions.

For P1=23 and n < = 1000, I can find no solutions.

For P1=29 and n < = 1000, I can find no solutions.

For P1=31 and n < = 1000, I can find no solutions.

For P1=37 and n < = 1000, I can find no solutions.

For P1=41 and n < = 1000, I can find no solutions.

For P1=43 and n < = 1000 other than n = 2, I can find no others.

For P1=47 and n < = 1000, I can find no solutions.

]]>I had a feeling it would be hard to find prime for n>6 for P1=2 and I quit looking for them and now knowing there is no prime for n up to 1000 it is just worthy not trying:)

]]>P1=13 and n=2

Ps={191, 251}

P1=43 and n=2

Ps={1931, 2111}

]]>There are three things that the prime has to match, a product, a sum and +- and when n becoming larger it would be harder to find the prime. This is what I believe and maybe a computational result would give a slightly different picture.

]]>P1 n

2, 4

2, 6

5, 4

5, 8]]>

Seems that for P1 = 2 that they are very rare.

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