However, a conceptual understanding of these concepts leads to insights that calculators and computers cannot provide.

When a number cannot be factored into a pair of smaller numbers then it is a prime number.

Mechanical use of mathematics is like using computer programs without understanding how they are put together.

I wanted to create a mathematical sequence that rhythmically, periodically increased in value by multiplication, as it oscillated in value by subtraction, at the same time.

Their distribution along the continuum of numbers appears to be random.

There are, however, formulas and diophantine equations that will calculate prime numbers.

There are algorithms that can calculate primes into the millions of digits.

But these prime-finding algorithms require a great deal of time and math to accomplish their task.

I humbly submit that Ive discovered a super-easy way to find and count prime numbers.

I dont know what this e q uation means for math, or number theory; I dont know if it will help solve the Riemann hypothesis, or if it works with the zeta function.

I just know that its a simple two-step equation that works to reliably reveal prime numbers.

And its kinda fun.

If you start with the number 2 and then you plug in each next integer (3, 4, 5, 6, 7, 8) into the equation, you can count your way up the continuum of prime numbers.

Never missing one.

In fact, its so easy that an 8-year-old with basic multiplication skills could find prime numbers with digits into the thousands and tens of thousands using just their smartphone calculator.

Im fairly certain that one could write a computer program using this equation that would find all of the prime numbers as high as you care to calculate.

Prime numbers seem to be arranged in overlapping wave patterns.

They rise and fall in these predictable rhythms.

From what I can tell, there are 5 waves of prime numbers.

Ultimately, they braid together to form the continuum of prime numbers, the one that appears random, but once you spot its pattern in the number sets, the distribution of prime numbers begins to look more like this: To calculate prime numbers, all you need to do is pick an integer.

Is it even, or is it odd Does it end in 0, or a 5 Or does it end in a 2 Those are the five waves.

There are the odd numbers: 3, 7, 9 There are the numbers that end in 5s or 0s.

Those are two prime numbers located on either side of a non-prime integer.

Integers ending in 0s and 5s, sometimes, but not always, calculate out as twin primes.

To find them, here are two solutions: If the integer ends in a 5, the equation is: 3(n) -2 and 3(n) 2 If the integer ends in a 0, the equation is: 3(n) -1 and 3(n) 1 So, there you go.

As the gap between the 0s and 5s of the prime wave patterns grows wider the multiples of seven and eleven overlap to fill in the gaps.

For instance, 3,810 ends in 0: (3 x 3810) -1 11,429 (isnt a prime number, its divisible by 11 x 1039) (3 x 3810) 1 11,431 (isnt a prime number, its divisible by 7 x 1633) This is where the deviation of the prime number pattern becomes evident.

The higher you climb up the number line the fewer prime numbers there are.

As the gaps between prime numbers begin to grow, the pattern repeats but with less frequency.

Numbers that end in zero often calculate out to be a non-prime numbers, typically divisible by 7 or 11.

There seems to be a pattern here, too.) I discovered this prime number wave equation purely by accident.

Prime Numbers List