def main():
import math
import trialDivision
i = 9
while 1:
successFlag = 1
if not trialDivision.main(i):
for j in range(1, math.ceil(math.sqrt(i // 2))):
if trialDivision.main(i - 2 * (j**2)):
successFlag = 0
if successFlag:
print(i)
break
i = i + 2
def main():
import trialDivision
maxChain = 0
storeI = 0
storeJ = 0
for i in range(-1000, 1000):
for j in range(-999, 999):
n = 0
while 1:
evaluate = (n * n + j * n + i)
if (evaluate <= 1):
if (n > maxChain):
maxChain = n
storeI = i
storeJ = j
break
if (trialDivision.main(evaluate) == 0):
if (n > maxChain):
maxChain = n
storeI = i
storeJ = j
break
n = n + 1
print(maxChain)
print(storeI)
print(storeJ)
def main():
import trialDivision
primeArray = []
for i in range(1,10000):
if (trialDivision.main(i) == 1):
primeArray.append(i)
primeAmount = len(primeArray)
relationGrid = []
for A in range(primeAmount):
truthVector = []
for B in range(primeAmount):
if concatenate(primeArray[A],primeArray[B]):
truthVector.append(1)
else:
truthVector.append(0)
relationGrid.append(truthVector)
for a in range(primeAmount):
for b in range(a+1,primeAmount):
if relationGrid[a][b] and relationGrid[b][a]:
for c in range(b+1,primeAmount):
if relationGrid[a][c] and relationGrid[c][a] and relationGrid[b][c] and relationGrid[c][b]:
for d in range(c+1,primeAmount):
if relationGrid[a][d] and relationGrid[d][a] and relationGrid[b][d] and relationGrid[d][b] and relationGrid[c][d] and relationGrid[d][c]:
for e in range(d+1,primeAmount):
if relationGrid[a][e] and relationGrid[e][a] and relationGrid[b][e] and relationGrid[e][b] and relationGrid[c][e] and relationGrid[e][c] and relationGrid[d][e] and relationGrid[e][d]:
print(primeArray[a])
print(primeArray[b])
print(primeArray[c])
print(primeArray[d])
print(primeArray[e])
def main():
import trialDivision
import itertools
import time
t = time.time()
i = 101
while i < 100000:
print(i)
numString = str(i)
for j in itertools.combinations(range(5), 2):
baseList = ["*", "*", "*", "*", "*", "*"]
baseList[j[0]] = numString[0]
baseList[j[1]] = numString[1]
baseList[5] = numString[2]
compositeCounter = 0
for m in range(10):
newList = [str(m) if x == "*" else x for x in baseList]
result = int(''.join(newList))
if (trialDivision.main(result) == 0) and (result > 100000):
compositeCounter = compositeCounter + 1
if compositeCounter > 2:
break
if (compositeCounter < 2) and (m == 9):
print(time.time() - t)
return result
i = i + 2
def main():
import trialDivision
import itertools
for i in range(1000, 10000):
if trialDivision.main(i):
numString = str(i)
perms = list(
set(list(''.join(p)
for p in itertools.permutations(numString))))
perms.sort()
perms = perms[1 + perms.index(numString):]
for j in perms:
if (trialDivision.main(int(j))
and trialDivision.main(2 * int(j) - i)
and (str(2 * int(j) - i) in perms)):
print(numString + j + str(2 * int(j) - i))
def main():
import itertools
import trialDivision
digitList = [1, 2, 3, 4, 5, 6, 7]
perms = itertools.permutations(digitList)
maxNum = 0
for i in perms:
numString = ''.join(str(j) for j in i)
num = int(numString)
if (trialDivision.main(num) == 1):
maxNum = num
print(maxNum)
def main():
import trialDivision
primes = 0
counter = 1
while (10 * primes) > (4 * counter - 3) or counter < 2:
diagNumber = (2 * counter - 1)**2
for i in range(4):
diagNumber = diagNumber + 2 * counter
if trialDivision.main(diagNumber) == 1:
primes = primes + 1
counter = counter + 1
print(primes / (4 * counter - 3))
return (2 * counter - 1)
def main():
import trialDivision
total = 0
ticks = 0
i = 10
while (ticks < 11):
if (trialDivision.main(i)):
forwardString = str(i)
backwardString = forwardString
successFlag = 1;
for j in range(1,len(forwardString)):
forwardString = forwardString[:-1]
backwardString = backwardString[1:]
if trialDivision.main(int(forwardString)) == 0 or trialDivision.main(int(backwardString)) == 0:
successFlag = 0
if successFlag:
print(i)
total = total + i
ticks = ticks + 1
i = i + 1
print(total)
def main(cap):
import trialDivision
primeList = []
for i in range(1,cap):
if trialDivision.main(i):
primeList.append(i)
sumList = []
total = 0
sumList.append(0)
for j in primeList:
total = total + j
sumList.append(total)
maxChain = 0
maxPrime = 0
for k in range(0,len(sumList)):
for l in range(maxChain+1,k+1):
if (sumList[k] - sumList[k-l])>cap:
break
if (trialDivision.main(sumList[k] - sumList[k-l])):
maxChain = l
maxPrime = sumList[k] - sumList[k-l]
print(maxChain)
print(maxPrime)
def circularPrimes(length):
import trialDivision
digitSet = [1, 3, 7, 9]
total = 0
for i in range(0, 4**length):
number = 0
for k in range(0, length):
number = number + (10**k) * digitSet[i % 4]
i = i // 4
primeFlag = 1
for j in range(0, length):
number = (10**(length - 1)) * (number % 10) + number // 10
if (trialDivision.main(number) == 0):
primeFlag = 0
break
if primeFlag:
total = total + 1
return total
def concatenate(int1,int2):
import trialDivision
return trialDivision.main(int(str(int1)+str(int2))) == 1