def S(N):
primes = soe(N//2+10)#[-1::-1]
s = 0
tmp = 0
tmp2 = 0
tmpp = 0
mini = 0
count = False
for p,q in combinations(primes,2):
#if p>3162:break
if p==tmpp:continue
if p*q>N:
if count and p!=tmpp:
#break
pass
else:
tmpp = p
count = True
continue
else:
count = False
tmpp=0
if tmp2!=p:
mini=0
tmp2=p
if q>mini:
mini+=3000
#print(p,q,end='\r')
t = M(p,q,N)
if t==0:
return s
else:
print(t)
s+=t
return s
def e060():
x = soe(10**4)
print('{:>4}'.format('start'))
for i in x:
print(str(i))
p1 = sorted(set(j for j in soe(10**4) if j>i and \
isprime(str(j)+str(i)) and isprime(str(i)+str(j))))
for j in p1:
p2 = sorted(set(k for k in p1 if k>j and \
isprime(str(j)+str(k)) and isprime(str(k)+str(j))))
for k in p2:
p3 = sorted(set(l for l in p2 if l>k and \
isprime(str(k)+str(l)) and isprime(str(l)+str(k))))
for l in p3:
p4 = sorted(set(m for m in p3 if m>l and \
isprime(str(m)+str(l)) and isprime(str(l)+str(m))))
if len(p4):
print( [i,j,k,l,p4[0],[i+j+k+l+p4[0]]])
return 1
def test(num,n):
p = soe(n+1)+[0]
j = 0
while p[j]!=0:
if num%p[j]==0:
num=num//p[j]
else:
j+=1
if num<n:
return True
else:
return False
def isprime3(num, primes = [2,3,5,7,11,13,17,19]):
if len(primes)==0:primes = [2,3,5,7,11,13,17,19]
if num<=primes[-1]:
if num in primes:return True
else:return False
for i in primes:
if num%i==0:return False
if num**.5<primes[-1]:return True
else:
p = soe(int(num**.5)-1)
if p[-1]==primes[-1]:return True
return isprime3(num,p)
def e134():
top = 10**6
bot = 5
tot = 0
primes = soe(top+1)
primes = primes[primes.index(bot):]
mini = 100;
for i, num in enumerate(primes):
if i>mini:
print(i/len(primes))
mini+=100
if i==len(primes)-1:
break
tot += findnum(num, primes[i+1])
return tot
def Euler_87():
prime1 = soe(maxp)
count = set()
x = 1
last = 0
for i in soegen(90):
tmp =i**4
if tmp>=top:break
print(i)
for j in soegen(400):
tmp=j**3+i**4
if tmp>=top:break
for k in soegen(8000):
tmp = k**2+j**3+i**4
if tmp == top:print('wtf')
if tmp<top:
count.add(tmp)
else:break
return len(count)
'''
from script.allsieve import primesfrom2to,soe a = soe(10**7)
Considering quadratics of the form:
n² + an + b, where |a| < 1000 and |b| < 1000
where |n| is the modulus/absolute value of n
e.g. |11| = 11 and |4| = 4
Find the product of the coefficients, a and b, for the quadratic expression
that produces the maximum number of primes for consecutive values of n,
starting with n = 0.
'''
#primes = maths.primesd(100000)
from script.allsieve import soe
#from script.isprime import isprime
from script.maths import isprime2 as isprime
primes = dict.fromkeys(soe(10**5),1)
def Euler_27(numa=1000,numb=1000):
big = 0
for a in range(-numa,numa):
print(a/1000,end='\r')
for b in range(-numb,numb):
n = 0
val = n**2+n*a+b
if isprime(val):
num = 0
while isprime(val):
num+=1
n+=1
val = n**2+n*a+b
if big<n:
big = n
def e123(top=pow(10,10)):
p = soe(10**6)
for n in range(len(p)):
if ((2*(n+1)*p[n])%(p[n]*p[n]) > top and n%2 == 0):
return n+1
from script.maths import primesd
from script.allsieve import soe
from math import sqrt
primes = soe(10**6)
pd = dict.fromkeys(primes,1)
nprime = [x for x in range(1,10**6,2) if not pd.get(x)]
def Euler_46():
b = True
t = False
print('start')
for check in nprime[2:]:
for i in primes:
if i>check:return check
for j in range(1,(check-i)):
if 2*j**2>(check-i+2):break
if i+2*(j**2)==check:t = True;break
if t:t = False;break
if __name__=='__main__':
print(Euler_46())
from script.maths import primesd
from script.allsieve import soe
from math import sqrt
primes = soe(10**6)
pd = dict.fromkeys(primes, 1)
nprime = [x for x in range(1, 10**6, 2) if not pd.get(x)]
def Euler_46():
b = True
t = False
print('start')
for check in nprime[2:]:
for i in primes:
if i > check: return check
for j in range(1, (check - i)):
if 2 * j**2 > (check - i + 2): break
if i + 2 * (j**2) == check:
t = True
break
if t:
t = False
break
if __name__ == '__main__':
print(Euler_46())