def f2(s): r=f(s) for i in r: if isprime(i): for j in r: if i<j and isprime(j) and 2*j-i in r and isprime(2*j-i) and j<2*j-i: print(i,j,2*j-i)
def g(n): if n%16==0: m=n//16 if m==1 or isprime(m): return True else: return False elif n%4==0: m=n//4 if m==1 or isprime(m): return True else: return False else: return isprime(n)
def S(n,d,a): islongN=lambda x:10**(n-1)<=x<10**(n) alld=sum(10**i for i in range(n))*d for i in product(range(10),repeat=a): for j in combinations(range(n),a): t=alld for k in range(a): t=t-(d-i[k])*10**j[k] if islongN(t) and isprime(t): yield t
def f(s): ## if s[2]==s[3]==0 and s[4]==1: ## print(s) for tem in maketem(): f=ft(tem,s) if tem[0]: mr=1 else: mr=0 if len([i for i in range(mr,10) if isprime(f(i))])>=8: print(tem,s) return False
def f(n): i=2 S=set() while i*(3*i-3)+1<n: j=i-1 while j>0: t=i**3-j**3 if isprime(t): S.add(t) if t>n: break j-=1 i+=1 return len(S)
def p179(): result=1#2,3 for i in range(3,10**7,2): if i%10000==1: print(i) if not isprime(i): a1=numofdivisors(i-1) a2=numofdivisors(i) a3=numofdivisors(i+1) if a1==a2: ## print(i-1,i) result=result+1 if a2==a3: ## print(i,i+1) result=result+1 return result
def fi(): a,b=0,1 first=1 mo=0 for i in range(100000): mo=mo+2 for j in range(3): first=first+mo if isprime(first): a=a+1 first=first+mo b=b+4 if i%1000==0: print(a,b) if b/a>10: return 2*i+3
def conisprime(n,m): return isprime(int(str(n)+str(m))) and isprime(int(str(m)+str(n)))
def prnums(l): return len([i for i in l if isprime(i)])