Anyone got a Degree in Mathematics / Number theory and willing to help Student- Legendre Conjecture)

yes no, but i hang goedel numbers on your things and put all in N and THEN i put on Mozart-theorem and it moves like you say and i can't read the numbers anymore from the fast and it goes maybe greyish? Maybe, but not when my numbers were red and your things were blue cuz that's purple just look it up go right ahead.

I also made a theorum. just at home.
it is: 0=1
just count how many 0? 1
so i am completely right. and you can also do a daisy chain like this
0=1=2=3=4=5=6=7=8=9=....
this is nice in the spring, or whatever. you can try it yourself.

@a_player thank you for your kind contibution. I am putting a lot of time and it isn't a waste of time because I am learning number theory. It annoys me that such a simple problem can't be solved!!!

i think that the problem stems from there being no definable relationship between the series of those squares and prime distribution. The gaps "happen" to be large enough to find primes in them when you "look" by calculation, but there simply can't be a formal proof, because primes and squares don't relate in any formal way, so you have to 'prove' it practically, forever. Goldbach conjecture is essentially the same issue, no relationship between primes and even numbers that can be formalised.

I must admit however that the twin-prime conjecture still plagues me at times. So I sympathise with the addicts:D

Dont u know and old theorem that says, that instead of guessing the prime numbers, u just pick them, and this will give u new paths into the logarithms, but u will have to create a new variable the variable of error, and then u will understand the constancy of the gaps, try it its very easy.

U need to break the number into Q, so that It flows more fast, because by working on N u are under constrainsts, and it loses a lot of speed its like it has enormous brakes, its like recursion,
u need the recursion feeling, so that it flows.

variable of errir is e
dey sey that's 2.71828 but what i jo is just not listen! clever from me.

you should read www.scientificamerican.com/article/what-is-godels-theorem/, it deals with godel theorem, maybe it can help you understanding why there is a LOT ( specially in number theory ) of conjecture which hasnt ( and probably whill never ) being prooved

@Irishman964
"Prove that rays of light that do not enter through the focus will always reflect through the focus of a parabola" its really, really, really easy ! nothing to compare with the conjecture we are talking about ! lets say you have a parabola P / y=ax² + bx +c, make a translation such that you can consider c = 0, then calculate the equation of the tangent at any point of P(x,y), then calculate the normal at his point ( easy since you know the tangent vector 'v' and the norma vectore w is / <w.v> = 0 ), then calculate the reflection of a light ray at its point rl = x ) and to conclude notice that all lines have a common point, which is called the focal point of a parabola ..