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Not at all!"A prime number is a number that has only two divisors: itself and the number one. Examples of prime numbers are: 1, ..."
That statement is contradictory.
1 has only two divisors (1 and itself).Number 1 does not have *two* divisors! Therefore 1 is not a prime number!
If you are going to count divisors more than once then every number has infinite divisors!
The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since "in exactly one way" would be false because any n==n.1. In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states "Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable." As more simply noted by Derbyshire (2004, p. 33), "2 pays its way [as a prime] on balance; 1 doesn't."
With 1 excluded, the smallest prime is therefore 2. However, since 2 is the only even prime (which, ironically, in some sense makes it the "oddest" prime), it is also somewhat special, and the set of all primes excluding 2 is therefore called the "odd primes." Note also that while 2 is considered a prime today, at one time it was not (Tietze 1965, p. 18; Tropfke 1921, p. 96).
Funny...Anonymous wrote:Oh you're right, how could I be so blind?kp wrote:1 has only two divisors (1 and itself).
1 has two divisors, 1 and 1!
I knew that 1 was a divisor but I forgot about 1!
Wait a minute! Actually 1 has three divisors: 1, 1 and 1. Or maybe five divisors, namely 1, 1, 1, 1, and, of course, 1.
Code: Select all
how funny....c
Code: Select all
#include<iostream>
#include<string>
using namespace std;
bool isprime(int n)
{
if(n==1) return 1;
if(n==2) return 1;
if(n%2==0) return 0;
for(int i=3;i*i<=n;i+=2)
{
if(n%i==0) return 0;
}
return 1;
}
int main()
{
string str1;
int prime;
while(cin>>str1)
{
prime=0;
for(int i=0;i<str1.size();i++)
{
if(str1[i]>='A' && str1[i]<='Z')
{
prime+=(str1[i]-'A'+27);
}
else if(str1[i]>='a' && str1[i]<='z')
{
prime+=(str1[i]-'a'+1);
}
}
if(isprime(prime)) cout << "It is a prime word.\n";
else cout <<"It is not a prime word.\n";
}
return 0;
}
Your code looks fine and it worked on all test cases I've tried it on (about 3M random cases).mhayter1 wrote:I too have have problems with this problem(WA). There are no test cases posted other than the ones on the problem, which my program outputs correctly. Can anyone give me test cases or find a problem in my code?
Code: Select all
Code has removed after getting AC.
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