The discovery goes beyond probing the distribution of prime numbers. “We’re actually nailing all the prime numbers on the nose,” Ono says. In this method, you can plug an integer that is 2 or larger into particular equations, and if they are true, then the integer is prime. One such equation is (3n3 − 13n2 + 18n − 8)M1(n) + (12n2 − 120n + 212)M2(n) − 960M3(n) = 0, where M1(n), M2(n) and M3(n) are well-studied partition functions. “More generally,” for a particular type of partition function, “we prove that there are infinitely many such prime detecting equations with constant coefficients,” the researchers wrote in their PNAS paper. Put more simply, “it’s almost like our work gives you infinitely many new definitions for prime,” Ono says. “That’s kind of mind-blowing.”