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Why is there no direct proof of the infinity of primes naturals sqrt2 after 2000 years?
Wiki User
∙ 16y ago
A direct proof of the infinity of primes would require what is essentially a formula to calculate the Nth Prime number; such a formula isn't even guaranteed to exist. It's possible to formulate a proof of the infinity of primes that would be, in a sense, direct. A direct proof that the square root of 2 is irrational is impossible, because the Irrational Numbers aren't defined in any direct way - just as the real numbers which aren't rational. So to prove that the square root of 2 is irrational, we have to prove that it's not rational, which requires indirect techniques.
Wiki User
∙ 16y ago
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Why have there been no direct proofs of the intinity of primes and naturals after 2000 years of study?
Sorry, but both of these have direct and relatively simple proofs. To prove the infinity of primes, let p1, p2, p3, ... pn be the first n primes. Form the product p1 x p2 x p3 ... x pn. Clearly it is divisible by all the prime numbers up to pn. Then add 1 to that sum. The new value cannot be divisible by any of the preceding primes so it must be a new prime number. Because you can do this for any value of n, the number of primes must be infinite. The proof of the irrationality of the square root of 2 is similarly easy and should be available in any high-school math book at the level of Algebra 2 or above.
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 proof for 1 by 0 is infinity?
If you mean 1 x 0, that's 0, not infinity.
What is the proof about multiplying twin primes and adding 1?
The question depends on what it is that you want to prove!
What is direct proof in geometry?
A direct proof in geometry is a proof where you begin with a true hypothesis and prove that a conclusion is true.
Is there proof of when Stonehenge was built?
There is no direct proof and dates are estimates.
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! :)
What is the subject of a direct geometric proof?
theorem
Is infinity a number?
No, infinity is not a number, in the mathematical sense. It is a symbol for "unlimited". As such it has uses in various theories in math and in physics. The simplest proof is adding a real value, such as 1, to infinity. Just as zero times any number is still zero, infinity plus any value will remain "infinity".
What is likely to be a subject of a direct geometric proof?
theorem
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.
What 2 prime numbers make 123?
There is no pair of prime numbers that sum to 123.Proof :Any two odd primes will sum to an even number, thus excluding 123 which is odd.Since 2 is the only even prime, the only possible solution is 2 + 121 = 123.But, 121 is not prime because it is 11 x 11.A similar proof shows that there is no pair of primes whose difference is 123.There are two primes that multiply to 123 : - 3 and 41.
