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Mathematicians hunting prime numbers discover infinite new pattern
- drdunce 1y agoThis have implications for public key cryptography?
- ysofunny 1y agoI 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.
- munichpavel 1y agoKen Ono, one of the authors, is the mathematician behind the University of Virginia women's swimming team's dominance in recent years, including world records and gold medals. https://news.virginia.edu/content/faculty-spotlight-math-professor-uva-swimmings-secret-weapon https://news.virginia.edu/content/faculty-spotlight-math-pro...
- noqc 1y agoBecause 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.
- deleted 1y ago[deleted]
- ijustlovemath 1y agoA 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.
- noqc 1y agoYou could not be more wrong, and I am in a very bad mood unrelatedly, so that is all I will say.
- ijustlovemath 1y agofeel free to expound once you're feeling regulated.
- noqc 1y agoA iff B exactly means "A is the only way for B to be true". The rest of your comment is gibberish.
- lupire 1y agoI have no idea what you are trying to say. What is "this" and what is the other "this"? A and B? What is an arbitrary A?
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- coderatlarge 1y agojust this quote from the article shocked me: “In 1976, Jones, Sato, Wada, and Wiens (2) (…) produced a degree 25 polynomial in 26 variables whose positive values, as the variables vary over nonnegative integers, is the set of primes.“
- coderatlarge 1y agohere’s an explicit formula: https://mathoverflow.net/questions/132954/the-jones-sato-wada-wiens-polynomial-for-prime-numbers-and-differential-calculus?utm_source=chatgpt.com https://mathoverflow.net/questions/132954/the-jones-sato-wad...
- coderatlarge 1y agojust to clarify this is well beyond my ability to verify or even situate in larger context.
- wewewedxfgdf 1y agoThis sort of thing makes me feel there is some deep understanding of reality only inches away from us, we glimpse it through these patterns but the secret remains hidden.
- cyanydeez 1y agoMakes me feel like math is mostly an arbitrary realm that after you've got 90% of the way in, the remaining 10% is just pointless coincidences.
- _feus 1y agoand it will be something so trivial and obvious, those who were looking for it will be kicking themselves for missing it
- seanmcdirmid 1y agoIt’s a huge refrain that shows up again every 20 years or so. Wolfram wrote a huge book with this premise, but I don’t think it’s gone anywhere even though it’s surely 25 years old by now.
- robin_reala 1y agoYou can read it for free at https://www.wolframscience.com/nks/ https://www.wolframscience.com/nks/ if you’re interested.
- burnt-resistor 1y agoGEB was similar in a cycle prior. It's cool to dream but the limits of accepted knowledge requires the hard work of assembling data, evidence, and reasoning.
- A_D_E_P_T 1y agoIt's arguably ~2500 years old, dating back to the Pythagoreans, who believed that "all is number" and had a very large and complex system of musical rituals. The modern manifestation is mostly the intellectual product of Konrad Zuse, who wrote "digital physics" in 1969. > https://en.wikipedia.org/wiki/Digital_physics https://en.wikipedia.org/wiki/Digital_physics Wolfram, Tegmark, Bostrom, etc. are mostly downstream of Zuse.
- andsoitis 1y agohttps://archive.is/2025.06.17-194128/https://www.scientificamerican.com/article/mathematicians-hunting-prime-numbers-discover-infinite-new-pattern-for/ https://archive.is/2025.06.17-194128/https://www.scientifica...
- gnabgib 1y agoPaper: https://www.pnas.org/doi/10.1073/pnas.2409417121 https://www.pnas.org/doi/10.1073/pnas.2409417121 (https://news.ycombinator.com/item?id=44323658 https://news.ycombinator.com/item?id=44323658)
- Sniffnoy 1y agoI'm a little confused at the significance here. Before I read the definition of the M_a, this seemed crazy, but on actually reading it, M_1 is just the sum-of-divisors function (usually denoted sigma). So, n is prime iff M_1(n)=n+1. That's much simpler than the first equation listed there! Indeed, looking things up, it seems that in general the functions M_a can be written as a linear combination (note: with polynomial coefficients, not constant) of the sigma_k (sigma_k is the sum of the k'th power of the divisors). So this result becomes a lot less surprising once you know that...
- boothby 1y agoI agree that the observation "M_1(n) = n+1 iff n is prime" is elementary. It certainly motivates some intuition behind the investigation in this paper, but I'd loathe to call it obvious. Note that the paper studies equations with polynomial coefficients on McMahon series. That is, the n+1 in our trivial observation is "stray" in a sense. For an at-a-glance indication of nontriviality, look no further than the conjecture associated with Theorem 1.2 -- that there are exactly five equations of this sort which are prime indicators. That seems spooky, to me; I can't help but wonder what structure underlies such a small number of relations.
- bubblyworld 1y agoCan you elaborate? How does this result become less surprising if you know that? Personally I would not have guessed that there are infinitely many characterisations of P involving sums-of-powers-of-divisors either.
- Sniffnoy 1y agoI mean, if you can do something a simple way, it's not that surprising that you can also do it a complicated way, I'd say.
- bubblyworld 1y agoIt's not surprising you can do exactly the same thing in more complex ways... but we're talking about infinitely many independent characterisations of P here.
- anthk 1y agoPrime generating functions in polynomials? That's almost Lisp domain. Mathematicians should play with Scheme and SICP.
- swayvil 1y agoYeah but can we get a pretty picture out of it? A cool fractal is worth a thousand words.
- nprateem 1y agoOh. (3n3 − 13n2 + 18n − 8)M1(n) + (12n2 − 120n + 212)M2(n) − 960M3(n) = 0. I'd have thought that was obvious.