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Let us start by presenting the sequence of odd numbers. 1,3,5,7,9,11,13,15…. Now let’s sum the first two terms of the sequence. 1+3=4 We now want to sum the first three terms of the sequence. 1+3+5=9 As you can see if we continue summing more and more terms of the sequence we get larger and larger …

Continue reading “An observation on odd numbers”

Conjecture no.25 There is more values of primes that make this set of finite polynomials( a1x^n+b1, a2x^n +b2, a3x^n+b3, …anx^n+bn ) generate more primes compared to another set of finite polynomials with the same amount of elements (a1x^n+c1, a2x^n +c2, a3x^n+c3, … anx^n+cn ) where (c1, c2 , c3, cn)< (b1, b2 , b3, bn). …

Continue reading “Conjecture no.25- A Conjecture on the Prime Number Races and some other disparate observations.-DISPROVED SEE COMMENTS BELOW!!!”

First, graph the quadratic polynomial, here I have graphed x^2. Next, draw a vertical line to touch the tip of the curve, although this image does not show it touching the curve it does in fact do so, here I graphed x=4 for the vertical line Now, draw a horizontal line that is equal to …

Continue reading “A simple way to integrate and differentiate quadratic polynomials.”

a^b is always transcendental when (a,b) are real transcendental numbers. A transcendental number is a number that is not the solution of a polynomial with integer coefficients. An example of a provably transcendental number follows. One such number that is transcendental by this is e^pi. The transcendence of e^pi was proven as a corollary of …

Continue reading “Conjecture no. 24 On Transcendental Numbers 2”

x/ln(n) – log(n) counts the primes between n^2 and (n+1)^2 fairly well. Here the x represents the difference between (n+1)^2 and n^2. The log in this case is considered to be a log to the base pi. It would be appreciated if someone could find a better approximating function. Some Approximations 233/144 is a good …

Continue reading “An approximate function for counting the primes between n^2 and (n+1)^2 and some approximations for irrational numbers and trigonometric functions.”

Between P^n and (P+2x)^n where n is equal to the difference of P+2x and P where P and P+2x are both prime , m being greater than zero there is at least P+2x – P primes. For example suppose P=3 then x=1 and n=2. Then 3, 3+2(1)=3,5 5-3=2 Now we will find that they are …

Continue reading “Conjecture 23. A conjecture based on Brocard’s Conjecture”

The Polya Conjecture is false over all Unique Factorization Domains. https://en.m.wikipedia.org/wiki/Unique_factorization_domain https://en.m.wikipedia.org/wiki/P%C3%B3lya_conjecture I welcome the readers to prove or disprove this conjecture. Thank you, Nunghead

There is only three primes of the form (6^n)^2 +1. Also are all the composite numbers of this form are squarefree Nunghead

Is there infinitely many primes such that p,p+2x is prime infinitely often where p is a regular prime. https://en.m.wikipedia.org/wiki/Regular_prime https://en.m.wikipedia.org/wiki/Polignac’s_conjecture As always I welcome the readers to prove or disprove this conjecture. Nunghead

There exists infinitely many triangular numbers that are prime. The triangular numbers are defined by adding n positive integers together. For example the first triangular number is 1 the next one is 3. The one after that is 6. So the triangular numbers are defined as 0+1=1 1+2=3 1+2+3=6 https://en.m.wikipedia.org/wiki/Triangular_number … As always I welcome …

Continue reading “Conjecture no.16 Triangular Numbers.-DISPROVEN-SEE COMMENTS BELOW.”