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There's no such thing as a "quadruple pair of primes". Assuming x is prime, one of x+2, x+4, and x+6 has to be nonprime. More specifically, one of them has to b
by jychang 13y ago
There's no such thing as a "quadruple pair of primes". Assuming x is prime, one of x+2, x+4, and x+6 has to be nonprime. More specifically, one of them has to be dividable by 3... If x mod 3 is 1, then x+2 is divisible by 3; otherwise, if x mod 3 is 2, then x+4 is divisible by 3.
- tempestn 13y agoGiven that a "pair of primes" simply refers to two primes within a fixed maximum distance of each other, not necessary separated by exactly 2, I assume a "quadruple of primes" would refer to the same thing. Not four numbers each separated by two, but four numbers all within a given distance of one another on the number line. (Whether this distance would be described as the total span encompassing all four numbers, or the maximum distance between any two of the four, I don't know.) And of course, you could generalize four to k, and quadruple to k-tuple.
- thedufer 13y ago>Whether this distance would be described as the total span encompassing all four numbers, or the maximum distance between any two of the four, I don't know. Actually, either one would imply a bound on the other (although a slightly looser one). If you know the total span, the same number is a looser bound on the maximum between any two of the four, and if you know the maximum of any two, 3 times that gives you a loose bound on the total span.
- tempestn 13y agoTrue. What I meant was, I'm just not sure which convention is commonly used when speaking of prime k-tuples.