abc conjecture | Agoh’s conjecture | Andrica’s conjecture | Carmichael condition | Chebyshev bias | Cramér conjecture | Eberhart’s conjecture | Euler’s criterion | Fermat quotient | Fermat’s little theorem | Fermat’s theorem | Gauss’s criterion | Gilbreath’s conjecture | Giuga’s conjecture | Grimm’s conjecture | Kummer’s conjecture | Landau’s formula | Lehmer’s totient problem | Mann’s theorem | norm theorem | prime Diophantine equations | prime distance | prime formulas | prime number | prime quadratic effect | Selfridge’s conjecture | Vandiver’s criteria | Wagstaff’s conjecture | Wilson quotient

The abc conjecture is a conjecture due to Oesterlé and Masser in 1985. It states that, for any infinitesimal ϵ>0, there exists a constant C_ϵ such that for any three relatively prime integers a, b, c satisfying a+bc, the inequality max(a, b, c)≤C_ϵ ∏_(pabc) p^(1+ϵ) holds, where pabc indicates that the product is over primes p which divide the product abc. If this conjecture were true, it would imply Fermat’s last theorem for sufficiently large powers. This is related to the fact that the abc conjecture implies that there are at least Clnx non‐Wieferich primes ≤x for some constant C. The conjecture can also be stated by defining the height and radical of the sum P:a+bc as h(P) | = | max{lna, lnb, lnc} r(P) | = | ∑_(pabc) lnp, where p runs over all prime divisors of a, b, and c.

math world wolframalpha-mathworld

Here is one of the trickiest unanswered questions in mathematics:

Can every even whole number greater than 2 be written as the sum of two primes?

read more there; https://plus.maths.org/

and regardless of the jump,

how does this connect to music… is this a possible example? sounds incredible anyhow!

http://www.opengoldbergvariations.org