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## #26 2013-01-22 09:06:38

Member
Registered: 2013-01-22
Posts: 128

### Re: Prime Numbers!!

For prime numbers (p), under 3 squared; p = 2a + 1 (where a = any whole number)
For prime numbers (r), under 5 squared; r = 3p +/- 2 or 4
For prime numbers (i), under 7 squared; i = 5r +/- 6 or 12 or 18 or 24
For prime numbers (m), under 11 squared; m = 7i +/- 30 or 60 or 90 or 120 or 150 or 180
For prime numbers (e), under 13 squared; e = 11m +/- 210 or 420 or 630 or 840 or 1050 or 1260 or 1470 or 1680 or 1890 or 2100

(A no. divisible by a, but not divisible by a group b +/- A no. divisible by group b, but not a = A no. not divisible by a or b.)

* Some rules give 1 but this is not prime.

"Time not important. Only life important." - The Fifth Element 1997

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## #27 2013-01-22 10:54:12

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Prime Numbers!!

Welcome to the forum!

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #28 2013-01-22 13:09:17

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Prime Numbers!!

Welcome to the forum!

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #29 2013-01-25 12:02:14

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

### Re: Prime Numbers!!

Prime numbers are numbers that have no other factors then one and itself. One is not a prime number... 1x1=1 and 1/1=1.
x = prime
y = anything other than 1 and x
z = composite
a = decimal
x/1=x. x/x=1. x/y=a.
z/1=z. z/z=1. z/y=y.
For something else on prime numbers... go to my Sieve of Eratosthenes post.

- n872yt3r
Math Is Fun Rocks!
By the power of the exponent, I square and cube you!

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## #30 2014-06-25 08:33:21

cmowla
Member
Registered: 2012-06-14
Posts: 61

### Re: Prime Numbers!!

kerr wrote:

http://en.wikipedia.org/wiki/Largest_known_prime_number
How is 17,425,170 a prime number? It is divisible by 2.
Thanks

It clearly says in plain English that this number is the number of digits of the largest known prime number.  You're welcome?

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## #31 2014-06-25 11:01:24

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Prime Numbers!!

Hi kerr;

is the prime number.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #32 2014-06-27 09:39:51

Member
Registered: 2013-01-22
Posts: 128

### Re: Prime Numbers!!

2+/-1..
6+/-1 5..
30+/- 1 7..
210 +/- 1 11..
2310 +/- 1 13..

equals primes......to a certain point above highest prime squared. e.g.>9,25,49,121 or 169 accordingly. And so on but the numbers get very big but you can do this up to infinity.

"Time not important. Only life important." - The Fifth Element 1997

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## #33 2014-08-16 02:50:25

Member
Registered: 2013-01-22
Posts: 128

### Re: Prime Numbers!!

The primes there are in a certain range can be estimated because there are;
1 No. not factorable by 2 in (2)
There are 2 No.'s not factorable by 2 or 3 in (6)
There are 8 No.'s not factorable by 2 or 3 or 5 in (30)
There are 48 No.'s not factorable by 2 or 3 or 5 or 7 or in (210)
times 48 by (prime -1) to get the next number of no.'s. i.e. =480 no.'s in (2310) not factorable by 2,3,5,7, or 11.....and so on.

"Time not important. Only life important." - The Fifth Element 1997

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## #34 2016-11-15 06:56:51

Gophne
Member
Registered: 2016-10-16
Posts: 26

### Re: Prime Numbers!!

Hi All

I am switching to this thread because I think this tread is more appropriate for posts dealing with primes. I have previously posted on the "help me" thread.

I am a small time prime hobbyist and have previously posted two "algorithms" that I have developed roughly on my own devices, although I have learned of similar formulations by other researchers/mathematicians, so my stuff might be "copies" or inferior models of what have already been done. I will post my first two "algorithms posted elsewhere on this site for information and comment/criticism!
#1
The 1st algorithm is a variation on the Sieve of Eratosthenes, but actually not a real sieve, but rather a combination of sieve and modulo operations. I discovered recently that there are similar sieves out there (e.g by David Turner of St Andrews University and others -See Wikipedia) so not too sure about the uniqueness of this algorithm therefore. However I did develop the sieve on my own, and I suspect it would be slightly different (and perhaps inferior) to the others. It involves the following; (#1) Take number line of positive integers, 1,2,3....... (#2) strike out all multiples of 2 leaving odd numbers (#3) Identify/mark "3" as a (new) prime number since "3" is not divisible by any positive integer (excluding "1") smaller than itself without leaving a remainder. Calculate square of the newly identified prime (9 in this case). For all odd numbers between 3 and 9 divide by the first prime "2" -all primes less that square root of 9,....nothing to eliminate since 4, 6 & 8 were already eliminated, leaving 5 & 7 as new primes. Now take next prime namely "5". Square of this prime is "25" Now divide all the (odd) numbers remaining on the number line between 9 & 25, by all the identified primes less than "5", namely "2" & "3" . "2" can actually be dropped since all the even numbers had already been eliminated from the number line. This operation eliminates "15,18 & 21", identifying 11,13,17,19 & 23 as primes. (#4) Now do the same for the odd numbers between "25" and the next prime (7=49), dividing with the identified primes less than the square root of (49=7), repeating this operation step by step. The beauty of this operation/algorith is that it identifies primes well ahead of the primes being used in the "sector" being appraised.

#2
My second algorithm is much more curious. We all know that the seemingly random distribution of primes have been a source of amazement to mathematicians for centuries, making it impossible to predict accurately a pattern or the next prime number. However, I have discovered that adding primes together in a particular way (in fact the summing operation of primes seem to produce many solid patterns)-namely consecutive sum of primes produces very REGULAR curves (with coefficients of determination(R^2) of "1" or close to "1"), using the regularity of the obtained curve to "predict" the next prime. This I can do to an accuracy which appear to be an improvement of the estimation provided by the Prime Number Theorum (PNT), and the curve functions anywhere in a series of prime numbers as opposed to the PNT which is more accurate as it approaches infinity. One of the summations is like this (consecutive sum); Add the first two together. Then to the sum add the next prime. To this sum add the next prime number and so on....(p+p), (p+p+p),(p+p+p+p).....This produces a curve of almost perfect slope, whereby it is possible to the predict the NEXT prime by using a trend line or the polynomial equation of the formula. If this curve is true one could potentially predict primes or the location of primes to great numbers. Although I tested the series of consecutive primes in the "Series Encylopedia(OEIS)" it exists, but graphing this series to determine prime numbers has not been done before I think.

I would appreciate further comment.

Last edited by Gophne (2016-11-15 06:59:16)

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## #35 2016-11-23 23:38:15

Member
From: Planet Mars
Registered: 2016-11-15
Posts: 620

### Re: Prime Numbers!!

There is also a formula first noticed by Leonhard Euler which proves that the set of primes is endless. The formula is
x²+x+41 is always a prime no. if x is an integer.

Practice makes a man perfect.
There is no substitute to hard work
All of us do not have equal talents but everybody has equal oppurtunities to build their talents.-APJ Abdul Kalam

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## #36 2016-11-24 03:00:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Prime Numbers!!

x²+x+41 is always a prime no. if x is an integer.

That is not always true. Try x = 41.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #37 2016-11-24 03:02:24

zetafunc
Member
Registered: 2014-05-21
Posts: 1,942
Website

### Re: Prime Numbers!!

There is also a formula first noticed by Leonhard Euler which proves that the set of primes is endless. The formula is
x²+x+41 is always a prime no. if x is an integer.

This cannot be true: just take x = 41 for instance, which clearly factorises into non-trivial factors. Euler found that this polynomial produces 40 distinct primes for the first 40 values.

In fact, it can be shown that such a polynomial cannot exist.

Last edited by zetafunc (2016-11-24 08:55:23)

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