import q27 import math if __name__ == '__main__': primes = q27.generatePrimeList(1000000) l = list(primes) l.sort() for x in range(9, 1000001, 2): if x in primes: continue flag = False for p in l: if p >= x: break y = math.sqrt((x - p) / 2) print(y) if y == int(y): flag = True break if not flag: print(x) break
import q27 if __name__ == '__main__': denom = sorted(list(q27.generatePrimeList(5000))) n = 2 while (1): total = [[0] * len(denom) for _ in range(n + 1)] total[0] = [1] * len(denom) #print(total) for i in range(1, n + 1): for j, x in enumerate(denom): x = total[i - x][ j] if i - x >= 0 else 0 #if the number includes the denominator x y = total[i][j - 1] if j >= 1 else 0 total[i][j] = x + y print(n, total[n][len(denom) - 1]) ways = total[n][len(denom) - 1] if ways >= 5000: break n += 1
import q72 import q27 if __name__ == '__main__': n = 10**7 primes = q27.generatePrimeList(n) spf = q72.seiveSpf(n) print("primes and seive calculation finished") mind = 10**99 minN = 0 for x in range(2, n + 1): if x in primes: continue y = q72.totient(x, spf) if sorted(str(x)) == sorted(str(y)): if x / y < mind: print(x, y) mind = x / y minN = x
import q27 import itertools def isArithmeticSeq(arr): return arr[0] + arr[2] == 2 * arr[1] if __name__ == '__main__': l = q27.generatePrimeList(10000) r = q27.generatePrimeList(1000) primeSet = l.difference(r) primes = list(primeSet) primes.sort() print(len(primes)) permutes = list( map(int, [''.join(x) for x in list(itertools.permutations(str(1487)))])) print(permutes) for x in primes: permutes = list( map(int, [''.join(x) for x in list(itertools.permutations(str(x)))])) count = 0 seq = set() for y in permutes: if y in primeSet: count += 1 seq.add(y) if len(seq) >= 3:
def checkP(n, primes, maxPrime): if n < maxPrime: return n in primes return is_prime(n) def checkCartConcatPrimes(a, b, primes, maxPrime): ij = int(str(a) + str(b)) ji = int(str(b) + str(a)) if not checkP(ij, primes, maxPrime) or not checkP(ji, primes, maxPrime): return False return True if __name__ == '__main__': primeset = q27.generatePrimeList(10000000) maxP = max(primeset) primes = sorted(list(q27.generatePrimeList(8500))) primes = primes[:8400] print(primes[:5]) print(len(primes)) pd = dict() for i in range(len(primes)): for j in range(i + 1, len(primes)): if checkCartConcatPrimes(primes[i], primes[j], primeset, maxP): if primes[i] in pd: pd[primes[i]].add(primes[j]) else: pd[primes[i]] = set() pd[primes[i]].add(primes[j])