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Q: Why would prime numbers work better for cryptography?
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Are most prime numbers also odd numbers?

All prime numbers are odd numbers. If one were even, it would be divisible by two and would, therefore, not be prime.


Why prime numbers are used in RSA algorithm?

Prime numbers are helpful in cryptography because it is MUCH easier to calculate the product (multiplication) of two prime numbers than to do the reverse process (find the prime factors of a big number). The bigger the prime numbers are, the higher the difference in time between calculating the product, or factoryzing this product back into the two prime numbers. When person A wants to tell B a secret, they could agree on two great prime numbers (in a secret way) and later use the product to communicate. A and B could easely calculate the other's factor because they know their own factor. Anyone else would have to try to factorize the huge prime number without any knowledge which would take, ideally, longer than 4.6 billion years (the age of the Earth). This is a VERY simplified answer and more can be found by googling around.


Is there any prime numbers that are square numbers?

No, there are no prime numbers that are also square numbers. Prime numbers are only divisible by 1 and themselves, while square numbers have integer square roots. Since the square root of a prime number is not an integer, a prime number cannot be a square number.


What number would be a counterexample to the following conjecture Prime numbers are odd?

2 would be a counterexample to the conjecture that prime numbers are odd. 2 is a prime number but it is the only even prime number.


What numbers would have less than two factors?

Prime numbers

Related questions

What would you prefer odd numbers or prime numbers?

Prime numbers.


What is the prime factors for numbers 849033451201111200500?

If you would be so kind as to put spaces between the numbers, we'd be better able to answer.


How do you find 2 prime numbers that if multiplied would generate a 400-digit number?

You seek for prime numbers that are approximately 200 digits big, then multiply them. I don't know details about the algorithms, but I understand that for cryptography, instead of using an algorithm that will be guaranteed to give a prime number, an algorithm is used, instead, that has a very, very high probability of giving a prime number. Probably this is done because it is faster.


Are most prime numbers also odd numbers?

All prime numbers are odd numbers. If one were even, it would be divisible by two and would, therefore, not be prime.


What are two prime numbers that if multiplied would generate a 400-digit number?

Any two prime numbers, of about 200 digits each, would work.Any two prime numbers, of about 200 digits each, would work.Any two prime numbers, of about 200 digits each, would work.Any two prime numbers, of about 200 digits each, would work.


Why prime numbers are used in RSA algorithm?

Prime numbers are helpful in cryptography because it is MUCH easier to calculate the product (multiplication) of two prime numbers than to do the reverse process (find the prime factors of a big number). The bigger the prime numbers are, the higher the difference in time between calculating the product, or factoryzing this product back into the two prime numbers. When person A wants to tell B a secret, they could agree on two great prime numbers (in a secret way) and later use the product to communicate. A and B could easely calculate the other's factor because they know their own factor. Anyone else would have to try to factorize the huge prime number without any knowledge which would take, ideally, longer than 4.6 billion years (the age of the Earth). This is a VERY simplified answer and more can be found by googling around.


When you write a number as a product of prime numbers?

A number as a product of prime numbers would be "x".


What kind of move would 16 be in the factor game?

Average. You'd have a one point lead. Prime numbers are better.


Are all multiples of a prime numbers prime numbers?

no, because then they would be divisible by the number you multiplied it by.


Why are prime numbers so important?

The reason why prime numbers are important practically is because of cryptography. Prime numbers are an essential part of what is called 'public-key cryptography'. In this technique two (massively massively large) prime numbers are multiplied together to generate a public key. Meanwhile the identity of exactly which two prime numbers are involved is kept secret (this is the private key). In the system you can use the public key to encode data and send it to me. But only I can decode that data because only I know the private key. This only works if prime numbers are involved. Otherwise a third party could come along and just start working out all the divisors of my public key and eventually crack which two (non-prime) numbers are the private key. When prime numbers are used, the third party can still try this method (called a brute force attack) but would have to try loads more numbers (because my public key only has two divisors - the two prime numbers - which by definition have no divisors of their own). This means that it would take a long time and wouldn't really be worth it. This technique forms the basis of most encryption over the internet (such as https). A website can send out its public key. The web page can then encode data and send it back to the website but it still can't be deciphered without the private key (even if the public key itself was intercepted).


Is there any prime numbers that are square numbers?

No, there are no prime numbers that are also square numbers. Prime numbers are only divisible by 1 and themselves, while square numbers have integer square roots. Since the square root of a prime number is not an integer, a prime number cannot be a square number.


Would the number 40 be good to start a factor board game?

No. Your opponent would have a 10 point lead. Prime numbers are better to start with.