satwnz

Bcz  we can find out any consecutive prime number by just subtraction of two numbers of series i.e Pn*, and Ipn.

Prime ={NPn*±IPn } i.e  30N±I5,

Prime Number range 5<=P<25, 

I5 have 2 AP series with  C.D=6,  and first element = 5 & 7

5,11,17,23….infinite, C.D=6, T1=5

7,13,19,25…..infinite, C.D=6, T1=7

in example below you can see with help of I5 AP series we can find all Prime Number range 5<=P<25

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%

.

.

.

.

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

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

.

.

.

.

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