Mathematicians hunting prime numbers discover infinite new pattern

Post by zck » Sat, Jun 21, 2025, 9:49 PM UTC

ysofunny wrote: post #56

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 firs…

Post by [deleted] » Sat, Jun 21, 2025, 11:37 PM UTC

noqc wrote: post #60

Because the article doesn't actually say so (presumably because the author doesn't know the difference between "if" and "if and only if") the statement: (3n^3 − 13n^2 + 18n − 8)M_1(n) + (12n^2 − 120n + 212)M_2(n) − 960M_3(n) = 0 is equivalent to the statement that n is prime. The result is that there are infinitely many such characterizing equations.

Post by cwmoore » Sun, Jun 22, 2025, 1:38 AM UTC

FredPret wrote: post #42

alphazard wrote: post #37

Earlier quoted context omitted.

If I handed you 1 apple, and then handed you another apple, you wouldn't be surprised to find that you had 2 apples. The same trick works with oranges and pears.

> If I handed you 1 apple, At this point I hold one object that we agree to label "apple". Note that even seeing it as a single object is a layer of abstraction. In reality it's a clump of fundamental particles temporarily banding together > and then handed you another apple, What's "another apple"? What does it have in common with the thing I'm already holding? We label this thing to be also an apple, but it's a tot…

Post by noqc » Sun, Jun 22, 2025, 3:12 PM UTC

ijustlovemath wrote: post #76

noqc wrote: post #60

Because the article doesn't actually say so (presumably because the author doesn't know the difference between "if" and "if and only if") the statement: (3n^3 − 13n^2 + 18n − 8)M_1(n) + (12n^2 − 120n + 212)M_2(n) − 960M_3(n) = 0 is equivalent to the statement that n is prime. The result is that there are infinitely many such characterizing equations.

A iff B doesn't mean "this is the only way for this to be true", it means A implies B and B implies A. B being the statement that a number is prime, but you can have any arbitrary A that is actually true.

Post by datameta » Sun, Jun 22, 2025, 3:23 PM UTC

thot_experiment wrote: post #74

datameta wrote: post #59

Earlier quoted context omitted.

To what extent are the Planck length and Planck second confirmed smallest discrete units?

I'm not a physicist, but I think those are the smallest units in the sense that they are the smallest units we could theoretically interact with/measure, not some hard limit. It's just that it's moot to consider anything smaller because there's no way for us to ever know.