/sci/ - Science & Math

>>11774976
what you wrote isn't exactly correct, because P(R=r) = 0 for a particular r, and conditioning on zero-probability event doesn't really make sense
but yes this is the idea

>>11774964
assume it is a rational number, then it's expansion in base 2 is periodic
from here https://en.wikipedia.org/wiki/Prime_gap use the statement "maximal prime gaps grow more than logarithmically..."
you will arrive at a contradiction