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I hope the twin prime conjecture will become a theorem during the remainder of my lifetime that's why I already got the double twin prime conjecture ready: th
by ysofunny 1y ago
I hope the twin prime conjecture will become a theorem during the remainder of my lifetime
that's why I already got the double twin prime conjecture ready:
there exists an infinite number of consecutive twin primes. 3 examples: 11,13; 17,19. 101,103;107,109, AND 191,193;197,199... I know of another example near the 800s
there's also the dubious, or trivial, or dunno (gotta generalize this pattern as well) of the first "consecutive" twin prime but they overlap which is 3,5 and 5,7.... which reminds me of how only 2 and 3 are both primes off by one; again, I need to generalize this pattern of "last time ever primes did that"
- D-Coder 1y agoBTW the phone number in Jenny's song, 867-5309, is a twin prime (867-5311).
- jsisto 1y agoTwin towers prime 9/11
- adgjlsfhk1 1y agoThe broader generalization you're headed towards is https://en.wikipedia.org/wiki/Dickson%27s_conjecture https://en.wikipedia.org/wiki/Dickson%27s_conjecture (or the even more general https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H https://en.wikipedia.org/wiki/Schinzel%27s_hypothesis_H) which basically say that the twin prime conjecture is true for every linear/polynomial generalization of twin primes.
- zck 1y ago> there's also the dubious, or trivial, or dunno (gotta generalize this pattern as well) of the first "consecutive" twin prime but they overlap which is 3,5 and 5,7.... which reminds me of how only 2 and 3 are both primes off by one; again, I need to generalize this pattern of "last time ever primes did that" For the triplet n, n+2, n+4, exactly one of those numbers is divisible by 3. So the only triplet n, n+2, n+4 where all numbers are prime contains 3: 3, 5, 7.