def findorderfractions2(x,a,b,c,d): lb = x*a/b+1 ub = x*c/d if isprime(x): return ub-lb+1 res = [1 for i in xrange(lb,ub+1) if gcd(i,x) == 1] return len(res)
def cl(num,mask): bits = len(str(num)) bm = mask nu = num if len(mask)<bits: mask = '0'*(bits-len(mask)-1)+mask+'0' for b in range(bits): if mask[b]=='1': nb = 10**(bits-b-1) num -= ((num/nb)%10)*nb #return [int(bm)*i*10 + num for i in range(10)] return len([1 for i in range(10) if (int(bm)*i*10 + num)>= nu and isprime(int(bm)*i*10 + num)])
def findmostCP(LIMITS): primes = [] sop = 0 gp = genprime() while sop < LIMITS: p = gp.next() primes.append(p) sop += p for n in range(1,len(primes)): for i in range(n+1): s = sum(primes[i:len(primes)-n+i]) if s < LIMITS and isprime(s): return s
def d(n): if n == 1: return (0, 1) w = [n * n - (n - 1) * k for k in range(1, 4)] return (len([p for p in w if isprime(p)]), 4)
def find2(): for n in range(9,0,-1): for numlist in permutations([str(i) for i in range(n,0,-1)]): if isprime(int(''.join(numlist))): return int(''.join(numlist)) return 0
def isnotcp(a,b): a,b = str(a),str(b) return not (isprime(int(a+b)) and isprime(int(b+a)))
def isop(com): for n in range(1,int(com**.5)+1): if isprime(com - 2*n**2): return True return False