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Composite numbers spread in same way as primes!


Victor Reijkersz

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I also posted the following in the sci.math newsgroup but got no responses that actually were interested in the main point of the "discovery" i thought i made.

would be happy if somewhere here could find the time to actually fill in the sieve of numbers as i am illustrating below:

Sieve of Vic?

I think i have discovered a more beautifull way to find the prime

numbers by using a Sieve. But i might be mistaken and have

rediscovered the wheel. My prime finding sieve method shows the

iterative nature of the primes very well and is therefore intriguing.

In short each primes causes an infinite number of other numbers to be

composite-numbers, but the composite numbers that are caused by each

prime are spread out in the exact same pattern as the primes

themselves are spread out.

 

 

I am not a mathimatican so please bare with me while I illustrate by

example instead of by formula. I would appreciate any serious

feedback. It might be I re-invented the wheel. I dont know. I dont do

maths often. only have been looking at primes as a sudoko puzzle. But

i thought i might actually have stumbled on an original thought. Hence

this post.

 

 

I am using a sieve approach for finding prime numbers. Just like

Eratosthenes. Noting all the numbers on a big sheet starting with 2

and numbering to however much you like.

 

 

Number 2 is the first prime in my mind. I note it on the primelist.

For every prime i find i have to cross out its power. 2 * 2 = 4. I

make a note on 4 that its the 1st composite-number caused by prime2.

 

 

Number 3 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power. 3*3=9. I make a note on 9

that its the 1st composite-number caused by prime3.

 

 

Number 4 is crossed out so its not a prime. Prime2 however left off

here. The pattern of prime 2 can now also be established. Its size is

1 because its the first pattern defined and its only pattern slot is 1

too. 1 because thats the difference between the first prime (2) and

the next (3). Knowing this pattern i know now the 2nd composite-number

caused by 2 must be current number(4) + (slot value(1) * prime(2)) =

6. I make a note on 6 that its the 2nd composite number caused by

prime2.

 

 

Number 5 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 5*5 =25. I make a note on 25

that its the 1st composite-number caused by prime5.

 

 

Number 6 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 3rd composite-number caused

by 2 must be current number(6) + (slot value(1) * prime(2)) = 8. I

make a note on 8 that its the 3rd composite number caused by prime2.

 

 

Number 7 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 7*7 =49. I make a note on 49

that its the 1st composite-number caused by prime7.

 

 

Number 8 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 4th composite-number caused

by 2 must be current number(8) + (slot value(1) * prime(2)) = 10. I

make a note on 10 that its the 4th composite number caused by prime2.

 

 

Number 9 is crossed out so its not a prime. Prime3 however left off

here. The pattern of prime 3 can now also be established. Its size is

1 because its the second pattern defined and its only pattern slot is

2. 2 because thats the difference between the second prime (3) and the

next (5).

Knowing this pattern i know now the 2nd composite-number caused by 3

must be current number(9) + (slot value(2) * prime(3)) = 15. I make a

note on 15 that its the 2nd compositie number caused by prime3.

 

 

Number 10 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 2 must be current number(10) + (slot value(1) * prime(2)) = 12. I

make a note on 12 that its the 5th composite number caused by prime2.

 

 

Number 11 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 11*11 =121. I make a note on

121 that its the 1st composite-number caused by prime11.

 

 

Number 12 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 2 must be current number(12) + (slot value(1) * prime(2)) = 14. I

make a note on 14 that its the 6th composite number caused by prime2.

 

 

etc... etc... for number 13 and number 14

 

 

Number 15 is crossed out so its not a prime. Prime3 however left off

here. Knowing this pattern i know now the 3rd composite-number caused

by 3 must be current number(15) + (slot value(2) * prime(3)) = 21. I

make a note on 21 that its the 3rd compositie number caused by prime3.

 

 

..etc.. etc..

 

 

Number 25 is crossed out so its not a prime. Prime5 however left off

here. The pattern of prime 5 can now also be established. Its size is

2 because its the third pattern defined and its pattern size is 2 with

the pattern slots being [2, 4] because thats respectivly the

difference between the third prime (5) and the next (7) and the next

one(7) and the next-next one(11).

Knowing this pattern i know now the 3rd composite-number caused by 5

must be current number(25) + (slot value(2) * prime(5)) = 25. I make a

note on 35 that its the 2nd compositie number caused by prime5.

 

 

etc.. etc...

 

 

Number 35 is crossed out so its not a prime. Prime5 however left off

here. Knowing this pattern i know now the 4th composite-number caused

by 5 must be current number(35) + (slot value(4) * prime(5)) = 55. I

make a note on 55 that its the 4th compositie number caused by prime5.

 

 

etc..

 

 

Number 55 is crossed out so its not a prime. Prime5 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 5 must be current number(55) + (slot value(2) * prime(5)) = 65.

Since this the third slot value we have look up for 5 and the pattern

size was only 2 we return here to slot 1. I make a note on 65 that its

the 5th compositie number caused by prime5.

 

 

etc..

ad infinitum...

 

 

TABLE OF PATTERN SIZE

Prime2 = 1

Prime3 = 1 (1*1)

Prime5 = 2 ( 2*1)

Prime 7 = 8 (4*2)

Prime 11= 48 (6*8)

Prime 13 = 480 (10*48)

Prime 17= 5760 (12*480)

Prime 19 = 92160 (16*5760)

Next pattern size is thus based on the ((current prime - 1 ) *

current pattern size)

 

 

TABLE OF SLOT VALUES OF PATTERNS

Number 2. [ 1 ]

Number 3. [ 2 ]

Number 5. [ 2, 4 ]

Number 7. [ 4, 2, 4, 2, 4, 6, 2, 6 ] (8 numbers)

Number 11. [ 2, 4, 2, 4, 6, ... ] (48 numbers)

Number 13. [ 4, 2, 4, 6, .. ] (480 numbers)

 

 

TABLE OF COMPOSITE NUMBERS CREATED BY PRIMES

Prime2 : 4,6,8,10,12,14,etc..

Prime3 : 9,15,21,27,33,etc...

Prime5: 25,35,55,65,85,95,115,125,etc...

Prime7: 49,77,91,119,etc...

 

 

i can be contacted too at v...@xs4all.nl

 

 

thanks for any feedback,

Vic

 

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I'm sorry, but I don't understand what "pattern size" and "slot values of patterns" are from your explanation.

 

 

Each prime has its own pattern.

For example for Prime7 its pattern is [ 4, 2, 4, 2, 4, 6, 2, 6 ]

 

Its pattern size is 8

The value of slot 1 of its pattern is 4

The value of slot 2 of its pattern is 2

etc...

the value of the last slot, slot 8, of its pattern is 6

 

The Pattern of Prime7 dictatates that the following numbers are composite numbers:

49,77,91,119,etc...

49 because its the square of 7

77 because its 49 + [ 4 * 7 ] (note that 4 is the 1st slot the pattern)

91 because its 77 + [ 2 * 7 ] (note that 2 is the 1st slot the pattern)

119 because its 91 + [ 4 * 7 ]

133 because its 119 + [ 2 * 7]

161 because its 133 + [ 4 * 7]

203 because its 161 + [ 6 * 7]

217 because its 203 + [ 2 * 7]

259 because its 217 + [ 6 * 7] note that 6 is the 8th slot the pattern)

...and the pattern repeats....

287 because its 259 + [ 4 * 7]

301 because its 287 + [ 2 * 7]

329 because its 329 + [ 4 * 7]

etc..

 

does this clear up what i mean with pattern, pattern size and slots of the pattern?

 

best regards,

Vic

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Okay, that's what I though. In that case, my question is how do you calculate the individual slots? I can see they are prime gaps, but how do you decide how many of them will play a role in the "pattern"? In the pattern for 7, you use 8 prime gaps, in the pattern for 11, you use 48 prime gaps..why? And also, how do you determine the prime gaps in advance of knowing which numbers are prime?

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Okay, that's what I though. In that case, my question is how do you calculate the individual slots?

 

the individual slots are equal to the gaps between the primes only for each prime we are calculating the slots for we have to shift 1 up.

 

 

so when calculating for the 1st prime (2) we start filling in the slots with first gap between primes (start at 1, the gap between 2 and 3).

gives the pattern [ 1 ]

 

when calculating for the 2nd prime (3) we start filling in the slots with second gap between primes (start at 2, the gap between 3 and 5).

gives the pattern [ 2 ]

 

when calculating for the 3rd prime (5) we start filling in the slots with third gap between primes (start at next 2, the gap between 5 and 7).

gives the pattern [ 2, 4 ]

 

when calculating for the 4th prime (7) we start filling out the slots with the fourth gap between primes (start at 4 , the gap between 7 and 11)

gives the pattern [ 4, 2, 4, 2, 4, 6, 2, 6 ]

I can see they are prime gaps, but how do you decide how many of them will play a role in the "pattern"? In the pattern for 7, you use 8 prime gaps, in the pattern for 11, you use 48 prime gaps..why?

Prime Number 2. pattern size 1

Prime Number 3. pattern size 1

Prime Number 5. pattern size 2

Prime Number 7. pattern size 8

Prime Number 11. pattern size 48

Prime Number 13. pattern size 480

the pattern size (or the number of slots) for a prime is equal to the pattern size of the previous prime multiplicated by the (previous prime minus 1).

for prime 3 its ((2-1)*1) = 1

for prime 5 its ((3-1)*1) = 2

for prime 7 its ((5-1)*2) = 8

for prime 11 its (7-1)*8) = 48

for prime 13 its (11-1)*48)= 480

etc..

 

And also, how do you determine the prime gaps in advance of knowing which numbers are prime?

 

Check the original post where i start at 2 and determine that 4 is a composite number because its the square of 2.

i then see that 3 is a number that has not been ruled a composite number by previous primes and i found the next prime.

Then arriving on 4, which we already know is a composite unique to 2, we know now the gap between the first 2 primes and can thus establish the pattern and pattern size for prime number 2 based on the info we now have.

the pattern size is of course 1 because its the first prime. and its one and only slot has value '1' because its the distance between the 1st and 2nd prime (2 and 3).

etc..

 

with the larger numbers we won't have found all the prime gaps neccessary to fill their slots, but thats not a problem because the patterns grow more rapidly then they are used up in having to determine new composite numbers.

 

again in the original post i take the reader by the hand in going through the sieve.

 

i hope this clarification again helps.

let me know if it does.

 

i tried this out on computer and it works. Up to a 6 digit numbers or so. This method finds the primes BEFORE it needs to know the gap sizes.

 

thanks again for taking the time to go over things. its really appreciated.

 

best regards,

Vic

 

 

Edited by Victor Reijkersz
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....

 

when calculating for the 3rd prime (5) we start filling in the slots with third gap between primes (start at next 2, the gap between 5 and 7).

gives the pattern [ 2, 4 ]

 

when calculating for the 4th prime (7) we start filling out the slots with the fourth gap between primes (start at 4 , the gap between 7 and 11)

gives the pattern [ 4, 2, 4, 2, 4, 6, 2, 6 ]

......

 

 

 

I do not understand why the pattern of 7 is 4,2,4....instead of 4,2,6...since you are using prime gaps and the 3rd gap is between 13 and 19. No?

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I do not understand why the pattern of 7 is 4,2,4....instead of 4,2,6...since you are using prime gaps and the 3rd gap is between 13 and 19. No?

 

Erm...since when is 17 composite?

 

Sorry for the delay in answering Vic, I completely forgot about this topic. I'm pretty tired at the moment, so I'm not all that excited about reading the whole thing again to remember what my argument was, but from what I do remember, your method requires remembering all the primes found thus far, to calculate the gaps (if not, I'm sorry, I really can't remember the method all that well). If that is the case, it is as effective, maybe even less, than the simplest algorithm for primes.

If on the other hand you wanted to prove that there was a connection between the distribution of primes and composites (I'm going to go on a whim and assume that's what you meant by "same way as"), and I'm not sure I see how your method proves that, that can be (I think) proven a lot faster. If you take the set of natural number and remove all primes, all that's left are composites (excluding the number 1). Furthermore, primes are the building blocks from which composite numbers are created, so I'd certainly expect there to be a connection between the two.

Please note however, I'm not an expert in this matter, far from it. Most of the above is just intuition working, so I apologize if it turns out to be gibberish. Also, I must say that's a pretty interesting way of generating primes. Thumbs up :)

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Erm...since when is 17 composite?

 

Sorry for the delay in answering Vic, I completely forgot about this topic. I'm pretty tired at the moment, so I'm not all that excited about reading the whole thing again to remember what my argument was, but from what I do remember, your method requires remembering all the primes found thus far, to calculate the gaps (if not, I'm sorry, I really can't remember the method all that well). If that is the case, it is as effective, maybe even less, than the simplest algorithm for primes.

If on the other hand you wanted to prove that there was a connection between the distribution of primes and composites (I'm going to go on a whim and assume that's what you meant by "same way as"), and I'm not sure I see how your method proves that, that can be (I think) proven a lot faster. If you take the set of natural number and remove all primes, all that's left are composites (excluding the number 1). Furthermore, primes are the building blocks from which composite numbers are created, so I'd certainly expect there to be a connection between the two.

Please note however, I'm not an expert in this matter, far from it. Most of the above is just intuition working, so I apologize if it turns out to be gibberish. Also, I must say that's a pretty interesting way of generating primes. Thumbs up :)

 

thanks. to be honest i am pretty buisy at the moment too. so thank you too for taking the time so far.

 

i am limiting my discussion of this algorithm to

http://tech.groups.yahoo.com/group/primenumbers/messages

for the moment.

 

somebody there actually pointed out to me that my sieve method predicts everything correctly until the number 1331 that it will say its prime while its not.

i think i can repair it though :) if i had some good sleep and some more time :)

 

but i welcome you to join up on the prime mailing list. i think its a better place for discussion since its more focussed on the topic

 

best,

vic

 

 

 

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  • 1 year later...

There is definitely a reason why the composites seem to be distributed the same as primes in the original sieve. In particular, what you described as

 

the composite numbers that are caused by each

prime are spread out in the exact same pattern as the primes

themselves are spread out.

 

If you examine your algorithm, you will see the list of composites in Prime2 are all numbers divisible by 2. This is obvious, of course.

 

All composites in your Prime3 as divisible by 3, but NOT by 2. All composites in your Prime5 list are divisible by 5, but not by 2 or 3.

 

Do you see what you are doing? You are simply filtering the set of integers for each subsequent iteration of the prime sieve, which artificially creates a sparser distribution for each subsequent prime sieve.

 

However, this uneven distribution does NOT match the distribution of primes in the original sieve. Whereas the original sieve results in an increasingly sparse distribution of primes, your sub-sieves necessarily have a repeating distribution because they are based on the fixed number of preceding primes.

 

For example, your Prime5 sieve shows composites divisible by 5 that are not divisible by 2 and 3. This means that these composites will simply start at 5*5 (25) and cycle every 30 integers (2*3*5). Thus: 25, 35, 55, 65, 85, 95, 115, 125, 145, etc. In other words, this distribution will not decrease in frequency like the prime sieve so therefore it is not the same.

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  • 4 years later...

So I am also not a mathematician, but I have discovered something similar. I split the composite numbers up by their prime factorization. So obviously primes are P1. Any number created by multiplying two primes together (i.e. 4, 6, 9) is P2. Any number created by multiplying three primes together (i.e. 8, 12, 14) is P3...and so forth. So now if you take the first (x) prime numbers and define a maximum P(n), you will only be able to create a finite amount of numbers (they are not consecutive). What is interesting is that you can determine how many numbers can be created. Again I'm not a mathematician so I'm not sure the proper notation, but what I have discovered is that the amount of numbers that can be created by specifying set amount of primes (x) to use and a maximum P(n) can be represented as:

 

x(n)/n!

 

or if you use http://www.wolframalpha.com

 

(pochhammer x,n)/n!

Edited by aekruse
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Surely that's just the number of ways one can choose n elements from a set of x elements if repetitions are allowed. You are just working out the number of ways that a set of numbers can be arranged - this is sometimes called the multiset

 

The Fundamental Theory of Arithmetics states that each number has a unique set of prime multiples (or is prime) - you are looking at using combinatrics to count the unique sets of primes and then multiplying them - same thing. Fraid this is not new - Euclid knew about the Fundamental Theory

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  • 1 year later...

There is definitely a reason why the composites seem to be distributed the same as primes in the original sieve. In particular, what you described as

 

 

 

If you examine your algorithm, you will see the list of composites in Prime2 are all numbers divisible by 2. This is obvious, of course.

 

All composites in your Prime3 as divisible by 3, but NOT by 2. All composites in your Prime5 list are divisible by 5, but not by 2 or 3.

 

Do you see what you are doing? You are simply filtering the set of integers for each subsequent iteration of the prime sieve, which artificially creates a sparser distribution for each subsequent prime sieve.

 

However, this uneven distribution does NOT match the distribution of primes in the original sieve. Whereas the original sieve results in an increasingly sparse distribution of primes, your sub-sieves necessarily have a repeating distribution because they are based on the fixed number of preceding primes.

 

For example, your Prime5 sieve shows composites divisible by 5 that are not divisible by 2 and 3. This means that these composites will simply start at 5*5 (25) and cycle every 30 integers (2*3*5). Thus: 25, 35, 55, 65, 85, 95, 115, 125, 145, etc. In other words, this distribution will not decrease in frequency like the prime sieve so therefore it is not the same.

Ipn series--- It is well define set of posative number.

Range of continues Prime ----It contains each and every prime number in fixed range.

No of Ipn sub series...This Ipn series have subseries it is also well define.

 

Common difference......As subseries are in A.P so common difference is given

% of Ipn element w.r.t. + Ve integer........it %of Ipn series wrt posative integer.i.e how many Ipn are in set of all +ve integer

 

Ex-I3( it is Ipn series) have one AP Serie and C.d = 2

3, 5, 7, 9, 11, 13------∞

i) Contain all primes and specific odd positive integer from 3 to infinite

ii) Continious prime 3≤P<9

ii) I3 Contain only 50.00% of positive integer

 

Ex-I5( it is Ipn series) have two AP Serie and C.d = 6

5 11 17 23 29 35 41 ------∞ (sub series 1)

7 13 19 25 31 37 43 -----∞ (sub series 2)

i) Contain all prime and specific odd positive integer from 5 to infinite

ii) Continuous prime 5≤P<25

ii) I5 Contains only 33.33% of positive integer

like this we can go for any series and any prime number.

br//

satish

I also posted the following in the sci.math newsgroup but got no responses that actually were interested in the main point of the "discovery" i thought i made.

would be happy if somewhere here could find the time to actually fill in the sieve of numbers as i am illustrating below:

 

Sieve of Vic?

I think i have discovered a more beautifull way to find the prime

numbers by using a Sieve. But i might be mistaken and have

rediscovered the wheel. My prime finding sieve method shows the

iterative nature of the primes very well and is therefore intriguing.

In short each primes causes an infinite number of other numbers to be

composite-numbers, but the composite numbers that are caused by each

prime are spread out in the exact same pattern as the primes

themselves are spread out.

 

 

I am not a mathimatican so please bare with me while I illustrate by

example instead of by formula. I would appreciate any serious

feedback. It might be I re-invented the wheel. I dont know. I dont do

maths often. only have been looking at primes as a sudoko puzzle. But

i thought i might actually have stumbled on an original thought. Hence

this post.

 

 

I am using a sieve approach for finding prime numbers. Just like

Eratosthenes. Noting all the numbers on a big sheet starting with 2

and numbering to however much you like.

 

 

Number 2 is the first prime in my mind. I note it on the primelist.

For every prime i find i have to cross out its power. 2 * 2 = 4. I

make a note on 4 that its the 1st composite-number caused by prime2.

 

 

Number 3 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power. 3*3=9. I make a note on 9

that its the 1st composite-number caused by prime3.

 

 

Number 4 is crossed out so its not a prime. Prime2 however left off

here. The pattern of prime 2 can now also be established. Its size is

1 because its the first pattern defined and its only pattern slot is 1

too. 1 because thats the difference between the first prime (2) and

the next (3). Knowing this pattern i know now the 2nd composite-number

caused by 2 must be current number(4) + (slot value(1) * prime(2)) =

6. I make a note on 6 that its the 2nd composite number caused by

prime2.

 

 

Number 5 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 5*5 =25. I make a note on 25

that its the 1st composite-number caused by prime5.

 

 

Number 6 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 3rd composite-number caused

by 2 must be current number(6) + (slot value(1) * prime(2)) = 8. I

make a note on 8 that its the 3rd composite number caused by prime2.

 

 

Number 7 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 7*7 =49. I make a note on 49

that its the 1st composite-number caused by prime7.

 

 

Number 8 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 4th composite-number caused

by 2 must be current number(8) + (slot value(1) * prime(2)) = 10. I

make a note on 10 that its the 4th composite number caused by prime2.

 

 

Number 9 is crossed out so its not a prime. Prime3 however left off

here. The pattern of prime 3 can now also be established. Its size is

1 because its the second pattern defined and its only pattern slot is

2. 2 because thats the difference between the second prime (3) and the

next (5).

Knowing this pattern i know now the 2nd composite-number caused by 3

must be current number(9) + (slot value(2) * prime(3)) = 15. I make a

note on 15 that its the 2nd compositie number caused by prime3.

 

 

Number 10 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 2 must be current number(10) + (slot value(1) * prime(2)) = 12. I

make a note on 12 that its the 5th composite number caused by prime2.

 

 

Number 11 is not crossed out so its a prime. I note it on the

primelist. I now also cross out its power 11*11 =121. I make a note on

121 that its the 1st composite-number caused by prime11.

 

 

Number 12 is crossed out so its not a prime. Prime2 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 2 must be current number(12) + (slot value(1) * prime(2)) = 14. I

make a note on 14 that its the 6th composite number caused by prime2.

 

 

etc... etc... for number 13 and number 14

 

 

Number 15 is crossed out so its not a prime. Prime3 however left off

here. Knowing this pattern i know now the 3rd composite-number caused

by 3 must be current number(15) + (slot value(2) * prime(3)) = 21. I

make a note on 21 that its the 3rd compositie number caused by prime3.

 

 

..etc.. etc..

 

 

Number 25 is crossed out so its not a prime. Prime5 however left off

here. The pattern of prime 5 can now also be established. Its size is

2 because its the third pattern defined and its pattern size is 2 with

the pattern slots being [2, 4] because thats respectivly the

difference between the third prime (5) and the next (7) and the next

one(7) and the next-next one(11).

Knowing this pattern i know now the 3rd composite-number caused by 5

must be current number(25) + (slot value(2) * prime(5)) = 25. I make a

note on 35 that its the 2nd compositie number caused by prime5.

 

 

etc.. etc...

 

 

Number 35 is crossed out so its not a prime. Prime5 however left off

here. Knowing this pattern i know now the 4th composite-number caused

by 5 must be current number(35) + (slot value(4) * prime(5)) = 55. I

make a note on 55 that its the 4th compositie number caused by prime5.

 

 

etc..

 

 

Number 55 is crossed out so its not a prime. Prime5 however left off

here. Knowing this pattern i know now the 5th composite-number caused

by 5 must be current number(55) + (slot value(2) * prime(5)) = 65.

Since this the third slot value we have look up for 5 and the pattern

size was only 2 we return here to slot 1. I make a note on 65 that its

the 5th compositie number caused by prime5.

 

 

etc..

ad infinitum...

 

 

TABLE OF PATTERN SIZE

Prime2 = 1

Prime3 = 1 (1*1)

Prime5 = 2 ( 2*1)

Prime 7 = 8 (4*2)

Prime 11= 48 (6*8)

Prime 13 = 480 (10*48)

Prime 17= 5760 (12*480)

Prime 19 = 92160 (16*5760)

Next pattern size is thus based on the ((current prime - 1 ) *

current pattern size)

 

 

TABLE OF SLOT VALUES OF PATTERNS

Number 2. [ 1 ]

Number 3. [ 2 ]

Number 5. [ 2, 4 ]

Number 7. [ 4, 2, 4, 2, 4, 6, 2, 6 ] (8 numbers)

Number 11. [ 2, 4, 2, 4, 6, ... ] (48 numbers)

Number 13. [ 4, 2, 4, 6, .. ] (480 numbers)

 

 

TABLE OF COMPOSITE NUMBERS CREATED BY PRIMES

Prime2 : 4,6,8,10,12,14,etc..

Prime3 : 9,15,21,27,33,etc...

Prime5: 25,35,55,65,85,95,115,125,etc...

Prime7: 49,77,91,119,etc...

 

 

i can be contacted too at v...@xs4all.nl

 

 

thanks for any feedback,

Vic

 

Me to intruded same funda for prime number find out

 

with mod 3#,5#,7#,11#

3#=6 gives all prime 3>=p<9

5#=30 gives all all prime 5>=p<=25

7#=210 gives all prime 7>=p<=49

11#=2310 gives all prime 11>=p<=121

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Pn#=...gives all prime Pn#>=p<=(Pn)^2

so we can find out any prime number in any range.Only thing is that i have required more advance compute which is comfortable with large numbers.

Br

satish kumar singh

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You're thinking of the Sieve of Eratosthenes. I mean, you literally just stole the name, then replaced it with your own. Nothing you did was new.

 

To make matters worse, you clearly lack any meaningful understanding of the topic, because your writing is as rambly as mine is when I am writing and thinking about a brand new topic to myself. I literally did the same thing last night with regards to fundamental algebra, associativity, and commutativity.

 

The sieve, as you mentioned, is formed by starting with two, marking it as prime, and then marking all the integer multiples of two as not prime. Then you proceed to the next number that isn't marked, if no number below it multiplies by an integer to yield it, then it is prime, and you mark off all integer multiples of that, then proceed to the next unmarked number.

 

Following those steps, you get the primes 2, 3, 5, and 7 rather quickly, you immediately mark off all evens, multiples of three, five, and seven. To top it all off, as showcased in the first image on the wikipedia, by following those steps you've already found all primes up to 113, inclusive.

 

In addition, your statement that the composites are distributed "in the same way as primes", well, actually all composites are spread in the exact opposite manner, since primes become less dense as you go up the number line, then composites must necessarily become more dense. In other words, your description is patently, obviously, false.

 

In short, if you want to be taken seriously, proof read and google the hell out of your idea. If you think your idea is ground breaking, and you're not a professional mathematician on the bleeding edge of knowledge, it's probably not. God knows I've made that mistake plenty of times.

Edited by Mathematical
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You're thinking of the Sieve of Eratosthenes. I mean, you literally just stole the name, then replaced it with your own. Nothing you did was new.

 

To make matters worse, you clearly lack any meaningful understanding of the topic, because your writing is as rambly as mine is when I am writing and thinking about a brand new topic to myself. I literally did the same thing last night with regards to fundamental algebra, associativity, and commutativity.

 

The sieve, as you mentioned, is formed by starting with two, marking it as prime, and then marking all the integer multiples of two as not prime. Then you proceed to the next number that isn't marked, if no number below it multiplies by an integer to yield it, then it is prime, and you mark off all integer multiples of that, then proceed to the next unmarked number.

 

Following those steps, you get the primes 2, 3, 5, and 7 rather quickly, you immediately mark off all evens, multiples of three, five, and seven. To top it all off, as showcased in the first image on the wikipedia, by following those steps you've already found all primes up to 113, inclusive.

 

In addition, your statement that the composites are distributed "in the same way as primes", well, actually all composites are spread in the exact opposite manner, since primes become less dense as you go up the number line, then composites must necessarily become more dense. In other words, your description is patently, obviously, false.

 

In short, if you want to be taken seriously, proof read and google the hell out of your idea. If you think your idea is ground breaking, and you're not a professional mathematician on the bleeding edge of knowledge, it's probably not. God knows I've made that mistake plenty of times.

Thanks for reply plz find support of my post

 

Ipn series--- It is well define set of posative number.

Range of continues Prime ----It contains each and every prime number in fixed range.

No of Ipn sub series...This Ipn series have subseries it is also well define.

 

Common difference......As subseries are in A.P so common difference is given

% of Ipn element w.r.t. + Ve integer........its %of Ipn series wrt posative integer.i.e how many Ipn are in set of all +ve integer start from some fix number

 

Ipn series Range of continues Prime No of Ipn sub series Common difference % of Ipn element

w.r.t. + Ve integer

I2 2 ≤ P < 4 1 2 100%

I3 3 ≤ P < 9 1 2 50%

I5 5 ≤ P < 25 2 6 33.33%

I7 7 ≤ P < 49 8 30 22%

I11 11 ≤ P < 121 48 210 20%

I13 13 ≤ P < 169 480 2310 19%

I17 17 ≤ P < 289 5760 30030 18%

I19 19 ≤ P < 361 92160 510510 17%

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IpN................ Tends to 0% means near abt all are primes

 

 

 

Ex-I3 have one AP Serie and C.d = 2

3, 5, 7, 9, 11, 13------∞

i) Contain all rpimes and specific odd positive integer from 3 to infinite

ii) Continious prime 3≤P<9

ii) I3 Contain only 50.00% of positive integer

Ex-I5 have two AP Serie and C.d = 6

5 11 17 23 29 35 41 ------∞

7 13 19 25 31 37 43 -----∞

i) Contain all prime and specific odd positive integer from 5 to infinite

ii) Continuous prime 5≤P<25

ii) I5 Contains only 33.33% of positive integer

 

br

satish kumar singh

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Thanks for reply plz find support of my post

 

Ipn series--- It is well define set of posative number.

Range of continues Prime ----It contains each and every prime number in fixed range.

No of Ipn sub series...This Ipn series have subseries it is also well define.

 

Common difference......As subseries are in A.P so common difference is given

% of Ipn element w.r.t. + Ve integer........its %of Ipn series wrt posative integer.i.e how many Ipn are in set of all +ve integer start from some fix number

 

Ipn series Range of continues Prime No of Ipn sub series Common difference % of Ipn element

w.r.t. + Ve integer

I2 2 ≤ P < 4 1 2 100%

I3 3 ≤ P < 9 1 2 50%

I5 5 ≤ P < 25 2 6 33.33%

I7 7 ≤ P < 49 8 30 22%

I11 11 ≤ P < 121 48 210 20%

I13 13 ≤ P < 169 480 2310 19%

I17 17 ≤ P < 289 5760 30030 18%

I19 19 ≤ P < 361 92160 510510 17%

.

.

.

.

IpN................ Tends to 0% means near abt all are primes

 

 

 

Ex-I3 have one AP Serie and C.d = 2

3, 5, 7, 9, 11, 13------∞

i) Contain all rpimes and specific odd positive integer from 3 to infinite

ii) Continious prime 3≤P<9

ii) I3 Contain only 50.00% of positive integer

Ex-I5 have two AP Serie and C.d = 6

5 11 17 23 29 35 41 ------∞

7 13 19 25 31 37 43 -----∞

i) Contain all prime and specific odd positive integer from 5 to infinite

ii) Continuous prime 5≤P<25

ii) I5 Contains only 33.33% of positive integer

 

br

satish kumar singh

 

I have no idea what you are arguing or pointing out. Yes, the density of primes decreases in the subset, [latex](0 , n)[\latex], of the integers decreases to zero as your right bound approaches infinity.

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