숫자를 한자리씩 옮겨도 모두 소수가 되는 숫자를 circular prime 으로 정의하기로 합니다. 예를 들면, 197은 197, 971, 719 세숫자가 모두 소수입니다.
100 이하의 circular prime 은 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97 총 13개가 있다고 합니다.
문제는 100만 이하의 수중에서 위 성질을 만족하는 circular prime의 갯수가 몇개인가 하는것입니다.
100 까지 소수 출력
1 2 3 4 5 | from sympy import isprimefor i in range(2,101): if isprime(i): print(i,"is prime") |
2 is prime 3 is prime 5 is prime ... 83 is prime 89 is prime 97 is prime
200까지 소수이면, circular number 생성
1 2 3 4 5 6 7 8 9 10 11 12 | from sympy import isprimefor i in range(2,201): if isprime(i): print(i,"is prime",end=",") string = str(i) is_circular_prime = True m=len(string) for i in range(1,m): string_new = string[i:]+string[:i] print(string_new,end=",") print() |
Circular number 가 소수인지 확인
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | from sympy import isprimefor i in range(2,201): if isprime(i): print(i,"is prime",end=",") string = str(i) is_circular_prime = True m=len(string) for i in range(1,m): string_new = string[i:]+string[:i] if isprime(int(string_new)): print(string_new,"is prime",end=",") else : print(string_new,"is not prime",end=",") is_circular_prime = False print("is_circular_prime ?",is_circular_prime) |
2 is prime,is_circular_prime ? True 3 is prime,is_circular_prime ? True 5 is prime,is_circular_prime ? True 7 is prime,is_circular_prime ? True 11 is prime,11 is prime,is_circular_prime ? True 13 is prime,31 is prime,is_circular_prime ? True ... 181 is prime,811 is prime,118 is not prime,is_circular_prime ? False 191 is prime,911 is prime,119 is not prime,is_circular_prime ? False 193 is prime,931 is not prime,319 is not prime,is_circular_prime ? False 197 is prime,971 is prime,719 is prime,is_circular_prime ? True 199 is prime,991 is prime,919 is prime,is_circular_prime ? True
1000 까지 Circular prime 출력
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | from sympy import isprimecount=0for i in range(2,1000): if isprime(i): #print(i,"is prime",end=",") string = str(i) is_circular_prime = True m=len(string) for j in range(1,m): string_new = string[j:]+string[:j] if not isprime(int(string_new)): is_circular_prime = False if is_circular_prime: print(i,"is circular prime") count+=1print(count) |
2 is circular prime 3 is circular prime 5 is circular prime 7 is circular prime 11 is circular prime ... 733 is circular prime 919 is circular prime 971 is circular prime 991 is circular prime 25
백만까지 계산
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | from sympy import isprimecount=0for i in range(2,1000000): if isprime(i): #print(i,"is prime",end=",") string = str(i) is_circular_prime = True m=len(string) for j in range(1,m): string_new = string[j:]+string[:j] if not isprime(int(string_new)): is_circular_prime = False if is_circular_prime: #print(i,"is circular prime") count+=1print(count) |
55
