/sci/ - Science & Math

>>10423694
suppose the stuff in the abs is positive for now
if P(x) = p prime, then x2 - 28x + 160 - p = 0
the roots of this polynomial are:

x_1/2 = 14 +- sqrt(142 - 160 + p)

these are rational iff 142 - 160 + p is a positive square number.
now we have check if there are any primes so p + 16 is square.

second case, the stuff in the abs is negative
P(x) = p prime, so -x2 + 28x - 160 - p = 0
x_1/2 = 14 +- sqrt(142 + 160 + p)
again, check if 356 + p is square

one has to additionally check that for each found prime the stuff inside the abs actually has the correct sign for the case. this probably means it cuts of a finite amount of the first case and almost all of the second. but i have not yet proven that.