"Remarkable" Pattern Discovered Behind Prime Numbers, Math's Most Unpredictable Objects
It "represents theoretical math that couldâve been done decades ago" - but it has big implications for the future.
can't really follow the math but makes a nice picture.
holy cow, that article is like 95% filler. this is the relevant part:
Itâs only now, however, that Ono and his teammates have noticed something incredible: that âthe prime numbers [âŚ] are the solutions of infinitely many special âDiophantine equationsâ in well-studied partition functions,â they explain in their new paper.Â
for example, the integer partitions of 4 will be 3+1, 2+2, 2+1+1, and 1+1+1+1
Hmmm...ok, sure...
Thatâs because partitions have a natural connection to a type of equation known as Diophantine equations â equations like Pythagorasâs or Markovâs, for which there are multiple if not infinitely many sets of rational solutions.
Diophantine equations are special because the interesting results are integer. For Pythagoras that would be something like 3, 4, 5 (32 + 42 = 52).
The story seems to be implying some connection between adding integers and prime numbers, but it never gets anywhere close to explaining that connection.
yup. no understanding to be gained. author probably doesn't either. picture looks interesting but no explanation of how it was generated. AI maybe
If you graph prime numbers in various ways, you get artifacts like rays or lines. But it's not related specifically to the prime numbers. They're just caused by the composite numbers erasing straight rows of integers, leaving behind straight rows of primes.