gaps.py

from collections import Counter

def primes(n):
	if n==2: return [2]
	elif n<2: return []
	s=range(3,n+1,2)
	mroot = n ** 0.5
	half=(n+1)/2-1
	i=0
	m=3
	while m <= mroot:
		if s[i]:
			j=(m*m-3)/2
			s[j]=0
			while j<half:
				s[j]=0
				j+=m
		i=i+1
		m=2*i+3
	return [2]+[x for x in s if x]

def distance(n):
    p = primes(n)
    differences = []

    for x in range(1,len(p)):
        differences.append(p[x]-p[x-1])

    print Counter(differences).most_common()

distance(100000) # (6, 1940), (2, 1224), (4, 1215)
# 6 is by far the most common difference between primes