prime is a Python script that calculates prime numbers and then looks for prime types.

prime.py

"""
Functions:
calc - calculate the specified number of primes starting with 2
findTypes - find the types in the current list of primes
"""

from math import sqrt

primeList = [2]
gapList = []
typeList = []

"""
Calculate the first n primes.

In:
n = number of primes to calculate
"""
def calc(n=1000):
    global primeList
    global gapList
    lastPrime = 2
    primeList = [lastPrime]
    gapList = []
    num = 3
    isPrime = 1
    while len(primeList) < n:
        sqrtNum = sqrt(num)
        for primeNumber in primeList:
            if num % primeNumber == 0:
                isPrime = 0
                break
            if primeNumber > sqrtNum:
                break
        if isPrime == 1:
            primeList.append(num)
            gapList.append(num - lastPrime)
            lastPrime = num
        else:
            isPrime = 1
        num += 2

"""
Find "prime types" with the specified parameters.
A "prime type" is a sequence of n primes, each within maxGap of
the next prime in the type.

In:
n = number of primes in type
maxGap = maximum difference between each consecutive prime in type
"""
def findTypes(n=2, maxGap=2):
    global primeList
    global gapList
    global typeList
    typeList = []
    idx = 0
    while idx + n - 1 < len(gapList):
        primeType = [primeList[idx]]
        isType = 1
        for i in xrange(0, n - 1):
            primeType.append(primeList[idx + i + 1])
            if gapList[idx + i] > maxGap:
                isType = 0
                break
        if isType == 1:
            typeList.append(primeType)
        idx += 1

calc()

print "# of primes: %i" % len(primeList)
print primeList

findTypes()

print "# of types found: %i" % len(typeList)
print typeList