Why is two the only even number that is prime?
Nov 3, 2014 — A prime number is such that it is divisible by only itself and one. Including 1 as a prime number would violate the fundamental theory of arithmetic, so in modern mathematics it is excluded. Two is a prime because it is divisible by only two and one. All the other even numbers are not prime because they are all divisible by two.
Determine whether a number is prime - Mathematics Stack …
How do I mathematically determine if a number is prime? If the number is n, then dividing it by every prime number less than or equal to sqrt(n) and showing that there is a remainder. There are a number of different sieve solutions for finding prime numbers, the oldest and most famous of which is the Sieve of Eratosthenes. These are generally ...
For how many positive integers $n$ is $4^n − 1$ a prime number?
Oct 26, 2017 — Sums of positive integers $2$ apart can be every composite number and never a prime. 5 A prime is not a product of primes, so why is “every positive integer, except 1, […] a product of primes”?
elementary number theory - If $a^4 + 4^b$ is prime, then $a$ is …
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elementary number theory - $n^4 + 4^n$ is a not a prime
Aug 14, 2019 — For any integer n greater than 1, $4^n+n^4$ is never a prime number. [duplicate] (3 answers) ...
Alternate definition of prime number - Mathematics Stack Exchange
For example, take $4$ (which clearly is not a prime): it is a factor of $16=8\cdot 2$, so I should check that either $4\mid 8$ or $4\mid 2$. But $4\mid 8$ is true. So $4$ is a prime, which is absurd.
Distribution of prime numbers modulo $4$ - Mathematics Stack …
Apr 22, 2019 — $\begingroup$ I’d recommend you read JOURNAL ARTICLE Prime Number Races (though I found an error: 93 is not prime) Andrew Granville and Greg Martin The American Mathematical Monthly Vol. 113, No. 1 (Jan., 2006), pp. 1-33 $\endgroup$ –
How to find number of prime numbers up to to N?
$\begingroup$ So let me get this straight: If I want to find the number or primes smaller than, say 10^100 - I'd have to first create a list of all primes smaller than 10^10, and then for every number (10^10,10^100) check them mod everything in said list (or against every member > sqrt(n) in that list)? $\endgroup$
Show that $n^4+4$ is not a prime number - Mathematics Stack …
Jan 27, 2015 — How do you show that for all $n ∈ N, n ≥ 2,$ $n^4 + 4$ is not a prime number? My attempt: I see that whatever number $n^4+4$ makes when $n$ is an even number ...
Primes in Gaussian Integers - Mathematics Stack Exchange
For instance, you can find it in the first 4 pages of Jurgen Neukirch's Algebraic Number Theory about the Gaussian integers. Also, LeVeque's Elementary Theory of Numbers has a short chapter dedicated to the Gaussian integers, where he proves this fact (see section 6.5).
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