The product of any two sequential primes, minus 1, is prime. Is this true?

[ultrafilter]

@cantara

Yes, since there are only 3 numbers in the set of sequential numbers that are primes…1,2,3 as noted above. The rest are not sequential, as they are separated by at least one number.

I’ve never heard that interpretation before. 3 and 5 are sequential primes because there are no primes between them.

[Giles]

@cantara

Yes, since there are only 3 numbers in the set of sequential numbers that are primes…1,2,3 as noted above. The rest are not sequential, as they are separated by at least one number.

The number 1 is not prime. It’s not prime, because if it were, various useful theorems (like the fact that every positive integer has a unique prime factorisation) would not work.

[OldGuy]

@wolf_meister

Its “corollary” states that any even number (greater than 6) is the sum of 2 primes. (Perhaps the latter is being referred to by the OP?)

Interesting. Does it perhpas state that every even number larger than 6 is the sum of two distinct primes? I ask becaue 6 = 3 + 3 and 4 = 2 + 2 so all of them would then be covered except 2 which is itself a prime.

[wolf_meister]

OldGuy
That’s already been discussed.
See Ultrafilter’s Posting #9

[ftg]

@wolf_meister

ftg
Seriously, I would have read more about it but unfortunately, (unlike you), I did not have a copy of Hardy and Wright’s “An Introduction to the Theory of Numbers” within arm’s reach.
I’m guessing the formulas must be rather complex or else you would have posted one.
Anyway, when I went to school (shortly after Pangaea seperated into distinct continents ), I was told there were no patterns to primes, no formulas, etc. Things must have changed quite a bit. Or maybe my ejukayshun wuz not of the highest kwality.

Hardy and Wright first came out in 1938. My edition (fifth) came out in 1979. Only small changes have been made over the years, with the newer stuff generally noted and “squeezed in” in smaller type, in footnotes, etc. So I think it’s original, esp. for something (that is first mentioned) in Chapter 1.

[EyesOnly]

When I was working on finding primes I realized that all primes can be broken down to 1. And a general sequence can be found. For example, 11+1=2, 112+1=3 1122+1=5 (112+1)*2+1=7 and any prime number can be found by adding these general sequences in appropriated order and then adding a set back prime. The only time it fails is when you reach the 19 23 hiccup, after which it continues to work until the 77 and 83 hiccup.

[Chronos]

I’m not sure I follow you there, EyesOnly. All numbers can be broken down to 1; you could say, for example, that 5 = 1+1+1+1+1. That’s pretty obvious, of course. You seem to be implying some more interesting pattern, but I’m afraid I can’t really see what it is.