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How many twin primes are there?
There are an infinite number of twin primes. This is true, but as yet there has not been published a valid proof of it. Perhaps soon someone will publish a valid proof.
What is the smallest prime?
The smallest positive prime is 2, but there is no smallest negative prime.One way to show this is to demonstrate that the cardinality of the set of negative primes is countably infinite (the proof will be similar to that for positive primes. Hint: use proof by contradiction. Assume a finite set of negative primes and derive a contradiction).Let me know if you'd like me to write up a formal proof that there is no smallest negative prime. I'll be happy to dig it out of one of my old homework sets! :)
Can an odd number be written as the sum of two primes?
If someone says it can't, here's a counter-example. 2 + 3 = 5 This is not a proof.
How do you prove space as infinite mathematically?
There is no mathematical proof that space is infinite. All we know is that there is an expanding limit to what we can see.
What is euclid's theory about prime numbers?
That there are an infinite number of prime numbers. Before we look an explanation or proof, we must agree on some points 1. The term number means whole number or integer 2. A prime number is any number that has only 2 factors (1 and itself). 3. All numbers are either prime or the product of 1 or more primes; try and find a number that you cannot generate as the product of primes (e.g. 8 = 2x2x2; 36 = 2x2x3x3). Now: If you take any two or more prime numbers and find their product the resulting number will have the prime numbers used as factors. However, if you add 1 to the number then the prime numbers you used to produce this number will now no longer be factors of this new number. Example 2,3,5 (first three prime numbers) 2x3x5 = 30 30 +1 =31 - now 2,3 and 5 are not factors as you will always have a remainder of 1 if you divide by any of the three original prime factors (2,3 or 5). If you take all of the known prime numbers and find the product of all of these prime numbers we get a new number (call it Product of Primes or PP), PP will have all the know primes as its factors. If we now add one to PP (PP + 1=N) we will get a number, N, that will have none of the known primes as a factor. If we say that the highest value prime number known (that we used to generate PP) is Pi then N must either be prime or have a prime factor greater than Pi and thus Pi is not the highest prime number. Therefore there are an infinite number of prime numbers.
