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How many prime numbers are theree?
There are an infinite number of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof:Suppose there are n prime numbers overall.Let N be a common multiple of all these primes.Is N+1 prime? If it is, we have found a new prime.Suppose N+1 is not prime. Thus, there exists a prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.(see the related link for a list of the first 500 prime numbers)
Do perfect numbers have to be prime numbers?
Perfect numbers cannot be prime numbers. Here's why:A number N is perfect if σ(N) = 2N (σ is the sum of divisors function). If there is a prime p that is a perfect number, then σ(p) = 2p. However, the only factors of p are 1 and p, so σ(p) is also equal to p+1. If 2p = p+1, then p=1, which is not prime, and 1 is defined to have only one factor, 1.
Twin prime numbers?
These are prime numbers of the form p and p+2.
How do you find the multiplicative inverse of a number mod a number?
Formally, a number n, has an inverse mod p only if p is prime. The inverse of n, mod p, is one of the numbers {0, 1, 2, ... , k-1} such that n*(p-1) = 1 mod p If p is not a prime then: if n is a factor of p then there is no such "inverse"; and if n is not a factor of p then there may be several possible "inverses".
What is m plus N plus p equals p plus n plus m?
It would be the same number either way because its addition.
How do you calculate prime factors?
Let n be the number whose prime factors we so desire to know. Required knowledge: All prime numbers less than sqrt(n).Test n for divisibility by each such prime numbers, starting with 2:If a prime number, p, is found to divide n, divide n by p, record p and continue (test for divisibility by p again) using n/p in the place of n.The recorded prime factors are the prime factors of n.
What is 25 P N less than 100?
The letters P N in this case stand for "prime numbers".
How many prime numbers exist?
There are an infinite amount of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof: # Suppose there are n prime numbers overall. # Let N be a common multiple of all these primes. # Is N+1 prime? If it is, we have found a new prime. # Suppose N+1 is not prime. Thus, there exists a prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.
How many prime numbers p are there such that 29 to the power p plus 1 is a multiple of p?
42
How many prime numbers are theree?
There are an infinite number of prime numbers. The first to have proven this was Euclid. Here are the general lines of his proof:Suppose there are n prime numbers overall.Let N be a common multiple of all these primes.Is N+1 prime? If it is, we have found a new prime.Suppose N+1 is not prime. Thus, there exists a prime number p which divides N+1 evenly. If p is one of the primes dividing N, it also divides 1 evenly, which is impossible. Thus, p is not one of the n primes, and we found a new prime.(see the related link for a list of the first 500 prime numbers)
Do perfect numbers have to be prime numbers?
Perfect numbers cannot be prime numbers. Here's why:A number N is perfect if σ(N) = 2N (σ is the sum of divisors function). If there is a prime p that is a perfect number, then σ(p) = 2p. However, the only factors of p are 1 and p, so σ(p) is also equal to p+1. If 2p = p+1, then p=1, which is not prime, and 1 is defined to have only one factor, 1.
True or false if two numbers a relatively prime one of the must be prime?
False. Consider 4 and 9. Neither are prime, but they have no common factors other than 1 and are therefore relatively prime. More generally, any two numbers p^n and q^n where p, q both prime and n<>p or q and n>1 are relatively prime. This is by no means all pairs of relatively prime numbers, but it's an easy way to find examples where neither of the pair is prime.
Does p plus 1 represent a prime or a composite?
As all prime numbers greater than zero are odd, p plus 1 would always be even, therefore always be dividable by 2 and therefore not prime
Why d you think prime numbers would be more useful for the creation of codes than composite numbers?
You are probably thinking of the RSA scheme, which requires the use of two large prime numbers. These numbers must be prime because calculations used to find the encrypting and decrypting key depends on the phi(N).N is the product of the two primes p and q.phi(N) is the number of positive integers m < N such that the greatest common divisor of m and n is 1.It has been proven that phi(N)= (p-1)(q-1).However, if p and q are not prime, then this equation is not true.In short, p and q keeps the prime factors large (for security) and N as small as possible (for simplicity).
Twin prime numbers?
These are prime numbers of the form p and p+2.
How do you find the multiplicative inverse of a number mod a number?
Formally, a number n, has an inverse mod p only if p is prime. The inverse of n, mod p, is one of the numbers {0, 1, 2, ... , k-1} such that n*(p-1) = 1 mod p If p is not a prime then: if n is a factor of p then there is no such "inverse"; and if n is not a factor of p then there may be several possible "inverses".
List prime numbers?
Prime Number Testevery prime number that you enter in the Prime Number Test is congruent to 1. If N is prime then P=1.
