Second Hardy-Littlewood Conjecture

range

The function

π(n)

gives the number of primes less than or equal to

n

. The second Hardy–Littlewood conjecture states that

π(x+y)-π(x)≤π(y)

for

x,y≥2

. The plot identifies

x

and

y

with pixel coordinates and renders

π(x+y)-(π(x)+π(y))

, with darker points corresponding to larger values.