# prime

1. ### neat prime observation

start with an even number E. between 1 and 2*E there will be a number such that both it and it+E are prime. after this, there will be a number such that, the low number from the previous pair + the high number from the previous pair, between that range, there will be another number such that it...
2. ### Prime ^ Fibonacci ^ partition numbers

What sequence arises from the intersection of prime, Fibonacci and partition numbers?
3. ### Prime number problem

Prove that there is always a prime number in interval [N,2N], for $N$ - positive integer. \exists p \; such that N\leq p \leq 2N.
4. ### prime number question

Find the smallest number n for which 11 divides 20n^(2)-1. For this question, I have made it so that 20n^2 is congruent to -1mod11; the quadratic residues of 11 are 1 goes to 1, 2 goes to 4, 3 goes to 9, 4 goes to 5, 5 goes to 3. But none of these contain the number -1, so -1 does not belong in...
5. ### Prime Numbers and the relationship between n and P_n

We often hear it said that either there is no relation between the natural, or counting numbers, $n$, and their counterparts the primes, $P_{n}$, or that if there is, it is so recondite as to be completely obscure. This is something of a sacred cow, but I don't believe it to be true. I'm not...
6. ### prime counting function

pi(n) = n/ln(n) + n/ln^2(n) + n/ln^3(n) + ... I think this is stronger than prime number theorem and closer to the true value of pi(n).
7. ### result of my prime counting function

pi(n) = number of primes less than n i proved that: pi(n) - pi(âˆšn) = n Ã— (1/2 Ã— 2/3 Ã— ... Ã— p-1/p) p = largest prime less than or equal to âˆšn prime number theorem: pi(n) = n/ln(n) lim pi(âˆšn) / pi(n) = lim âˆšn/ln(âˆšn) / n/ln(n) = lim 2/âˆšn = 0 => pi(n) - piâˆšn ~ pi(n) = n Ã—...
8. ### Computer program for printing Prime numbers in reverse order.

https://www.rapidtables.com/math/number/prime_numbers.html I would like to write a computer program which will print prime numbers starting from 100 till 0. i.e. reverse order. Can I get the source code written in any programming language C,C++,Java,C#, Python etc? Thanks & Regards, Prashant...
9. ### Prime number property

Let p_n be the n-th prime . Is the difference of p_{n+1} and p_{n} unlimited or not ? Example : 3-2=1 , 23-19=4 ...etc
10. ### Proof of twin prime conjecture

PROOF OF THE TWIN PRIME CONJECTURE The twin prime conjecture states that there are an infinite number of twin primes. Twin primes are a pair of primes that differ by 2 e.g. 11 and 13, 17 and 19, 29 and 31. Consider the sieve of Eratosthenes acting on the infinite number line. 2 makes the first...
11. ### Mystery of prime numbers solved

Proof of famous unsolved questions like Riemann Hypothesis, Goldbach's conjecture, twin prime conjecture, Polignac's conjecture, Brocard's problem, Oppermann conjecture and many more can be found in this book. Also in this book there is theory which can be treated as missing part of theory of...
12. ### Prime Factorization of very large integer with quadratic residue and its square roots

We have a very large modulus integer n also we have very large number y we know that y is a quadratic residue modulus n.Also we know all 4 square roots of y. What is the best way of prime factorization of n ?
13. ### What is a Rational prime?

Hello When we say let $p$ be rational prime, automatically that does mean that p>0?? thanks
14. ### How to generate prime numbers without the sieve of Eratosthenes??

Looping aâ¿â»Â¹ mod n=1 The output is Primes and pseudo Primes (carmichael) After (a being the base), tested that the algo works only if a = (n-1). for exemple n=7 1^7mod 7=1 2^7mod 7=1 3^7mod 7=1 4^7mod 7=1 5^7mod 7=1 6^7mod 7=1 prime n=9 1^9mod 9=1 2^9mod 9=4 3^9mod...
15. ### Prime numbers in base 6

I did an online search and found a couple of references, but nothing that pursued this in any depth. First of all, it seems that considering primes in base 6 would be a very useful teaching tool - an introduction to prime numbers - as it clearly illustrates both how 2 and 3 are the basis for...
16. ### The number of a number in the prime factorization of a factorial

How do we find, for example, how many '5's there are in the prime factorization of n! ? I've read that it's floor(n/5), but why is that? Thanks a lot.
17. ### Prime Number Sequence

Has someone study previously the following structure/pattern in prime numbers: a) genesis 1 (1) - > the numbers in the parenthesis indicates the pattern in the consecutive differences between the elements of the sequence, in this case the infinite set of integer numbers, from 1 to...
18. ### Prime number question

1) Show there are infinitely many odd prime numbers p=2n-1 2) Show that number two (2) is the only even prime number p=2
19. ### Prime number solution

I have come across the following question Find all integers n such that |2n^3-6n^2+4n+3| is prime My attempt is this is the maximum I could reach 2n^3-6n^2+4n+3 => 2n^2(n-3)+4n+3 => 2n^2(n-3) +(n-3)+ (3n+6) => (2n^2+1)(n-3)+3(n+2) How should I proceed further? Is it that I have to find the...
20. ### The relationships between Prime number and Fibonacci number (Part 2)

This is the upgrading of my first research with the same subject, which can be found in https://www.linkedin.com/pulse/relationships-between-prime-number-fibonacci-thinh-nghiem/?lipi=urn%3Ali%3Apage%3Ad_flagship3_profile_view_base_post_details%3BCuXz0krLTjSmIWUuweQOBg%3D%3D My conclusion...