PrimeGrid
Please visit donation page to help the project cover running costs for this month

Toggle Menu

Join PrimeGrid

Returning Participants

Community

Leader Boards

Results

Other

drummers-lowrise

Advanced search

Message boards : General discussion : Is there a pattern to prime numbers?

Author Message
AT Hiker
Send message
Joined: 14 Aug 12
Posts: 107
ID: 161744
Credit: 261,007,878
RAC: 0
Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (31,368)PPS LLR Ruby: Earned 2,000,000 credits (2,246,230)SR5 LLR Silver: Earned 100,000 credits (235,339)SGS LLR Gold: Earned 500,000 credits (500,635)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (513,917)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,590,640)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,724,311)TRP Sieve (suspended) Gold: Earned 500,000 credits (557,005)AP 26/27 Emerald: Earned 50,000,000 credits (50,040,211)GFN Double Bronze: Earned 100,000,000 credits (104,568,221)
Message 65891 - Posted: 25 May 2013 | 18:55:30 UTC

The answer to subject question I assume is no since if there was, finding all prime numbers would be simple.

But, can we be sure there is no pattern to prime numbers?

PS I am not a math person!
____________
https://signature.statseb.fr/sig-2259.png

Profile Crun-chiProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Nov 09
Posts: 3070
ID: 50683
Credit: 63,378,402
RAC: 268
Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 65894 - Posted: 25 May 2013 | 19:52:12 UTC - in response to Message 65891.

I also question that question to myself :)
And if pattern exist it is beyond our knowledge.
And I found "pattern" in two numbers...
look at this

1 pair
15*2^2785940+1
17*2^2721830-1

2785940-2721830= 64110

2 pair
15*2^2988834+1
17*2^2946584-1

2988834-2946584= 42250

3 pair
15*2^3162659+1
?
So if you follow pattern 64110, 42250, then third one will be in range 20000-30000
so next 17*2^N-1 will be in range 3132659 to 3142659
In that range is about 373 candidates so that can be processed in day or two..
good luck! and inform if you find something :)


____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie!

Profile DaveBProject donor
Avatar
Send message
Joined: 20 Jun 09
Posts: 351
ID: 42198
Credit: 11,898,570
RAC: 0
321 LLR Gold: Earned 500,000 credits (547,769)Cullen LLR Silver: Earned 100,000 credits (158,867)PPS LLR Silver: Earned 100,000 credits (162,534)PSP LLR Silver: Earned 100,000 credits (134,373)SoB LLR Gold: Earned 500,000 credits (510,012)SR5 LLR Silver: Earned 100,000 credits (266,757)SGS LLR Gold: Earned 500,000 credits (510,560)TRP LLR Silver: Earned 100,000 credits (242,439)Woodall LLR Gold: Earned 500,000 credits (508,989)321 Sieve (suspended) Silver: Earned 100,000 credits (200,123)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (229,801)PPS Sieve Ruby: Earned 2,000,000 credits (4,317,221)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (21,147)TRP Sieve (suspended) Silver: Earned 100,000 credits (333,494)AP 26/27 Bronze: Earned 10,000 credits (24,117)GFN Ruby: Earned 2,000,000 credits (3,730,320)
Message 65898 - Posted: 25 May 2013 | 21:00:59 UTC - in response to Message 65894.

There are many patterns to PROBABLE prime numbers.

1) All prime numbers greater than 3 are a multiple of 6 +- 1.
Proof : any number can be written as 6n+{-1,0,1 2 3 4), as 6 is even 6n is even and 6n+{0,2,4} is even and not prime, 6 is divisible by 3 so 6n+{0,3} cannot be prime, leaving 6n+-1 as possible prime numbers. Not all numbers 6n+-1 are however prime, e.g. 25 is composite but 6*4+1.

Note 6n+{x,y...} means 6 times something plus one of the numbers in the braces.

2) Euclid proved that if a continuous series of prime numbers are multiplied and then 1 is added the result will be prime, this is the original proof of an infinite numbers of primes. Not all primes fit into this series though.

Many other more maths based theories are out there. It is on these that the LLR method is based for example, the study of these is considered by some to be one of the most interesting subjects in maths.
____________
Member team AUSTRALIA
My lucky number is 9291*2^1085585+1

AT Hiker
Send message
Joined: 14 Aug 12
Posts: 107
ID: 161744
Credit: 261,007,878
RAC: 0
Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (31,368)PPS LLR Ruby: Earned 2,000,000 credits (2,246,230)SR5 LLR Silver: Earned 100,000 credits (235,339)SGS LLR Gold: Earned 500,000 credits (500,635)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (513,917)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,590,640)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,724,311)TRP Sieve (suspended) Gold: Earned 500,000 credits (557,005)AP 26/27 Emerald: Earned 50,000,000 credits (50,040,211)GFN Double Bronze: Earned 100,000,000 credits (104,568,221)
Message 65909 - Posted: 26 May 2013 | 3:27:31 UTC


How about a pattern involving the spacing of prime numbers?
____________
https://signature.statseb.fr/sig-2259.png

Profile [DPC]CamulosProject donor
Send message
Joined: 23 Mar 11
Posts: 86
ID: 91898
Credit: 105,677,919
RAC: 7,462
321 LLR Gold: Earned 500,000 credits (650,015)Cullen LLR Gold: Earned 500,000 credits (820,374)ESP LLR Gold: Earned 500,000 credits (550,246)Generalized Cullen/Woodall LLR Gold: Earned 500,000 credits (607,632)PPS LLR Jade: Earned 10,000,000 credits (11,146,743)PSP LLR Gold: Earned 500,000 credits (539,445)SoB LLR Gold: Earned 500,000 credits (627,950)SR5 LLR Amethyst: Earned 1,000,000 credits (1,023,449)SGS LLR Ruby: Earned 2,000,000 credits (2,389,355)TRP LLR Gold: Earned 500,000 credits (523,441)Woodall LLR Gold: Earned 500,000 credits (718,450)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (4,084,280)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (510,148)PPS Sieve Sapphire: Earned 20,000,000 credits (41,714,774)TRP Sieve (suspended) Gold: Earned 500,000 credits (560,644)AP 26/27 Turquoise: Earned 5,000,000 credits (5,336,760)GFN Sapphire: Earned 20,000,000 credits (33,510,955)PSA Silver: Earned 100,000 credits (357,578)
Message 65914 - Posted: 26 May 2013 | 8:25:26 UTC

@AT Hiker: If you could predict spacing between prime numbers; then primegrid would become obsolete.. and prime numbers with billions of digits could be calculated.

To cheer you up.. there are several visualizations for prime number gaps :)
Check out:
- Ulam Spirals
- Sieves of Chaos
____________
Member of the Dutch Power Cows
My Stats

Profile S@NL - FilmFreakProject donor
Avatar
Send message
Joined: 29 Nov 05
Posts: 58
ID: 1587
Credit: 3,290,496
RAC: 0
321 LLR Silver: Earned 100,000 credits (235,773)PPS LLR Gold: Earned 500,000 credits (512,812)SR5 LLR Gold: Earned 500,000 credits (508,431)SGS LLR Bronze: Earned 10,000 credits (71,624)TRP LLR Bronze: Earned 10,000 credits (82,218)Woodall LLR Bronze: Earned 10,000 credits (10,077)PPS Sieve Amethyst: Earned 1,000,000 credits (1,755,489)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Bronze: Earned 10,000 credits (90,725)
Message 65967 - Posted: 27 May 2013 | 11:42:13 UTC - in response to Message 65909.

AT Hiker wrote:
How about a pattern involving the spacing of prime numbers?

I just read an article about Zhang's Theorem on Bounded Gaps Between Primes stating he proved there will always be prime gaps < 70 million. Too large to make PG obsolete...
____________
Life is short and meaningless, unless you make the best of it.
http://server.by014.net/~weezepoe

AT Hiker
Send message
Joined: 14 Aug 12
Posts: 107
ID: 161744
Credit: 261,007,878
RAC: 0
Generalized Cullen/Woodall LLR Bronze: Earned 10,000 credits (31,368)PPS LLR Ruby: Earned 2,000,000 credits (2,246,230)SR5 LLR Silver: Earned 100,000 credits (235,339)SGS LLR Gold: Earned 500,000 credits (500,635)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (513,917)PPS Sieve Double Bronze: Earned 100,000,000 credits (100,590,640)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,724,311)TRP Sieve (suspended) Gold: Earned 500,000 credits (557,005)AP 26/27 Emerald: Earned 50,000,000 credits (50,040,211)GFN Double Bronze: Earned 100,000,000 credits (104,568,221)
Message 65981 - Posted: 27 May 2013 | 14:39:12 UTC

Thanks to all who replied.

The visualizations on Primal Chaos site are really neat.

I assumed from the start that there was no "known" pattern to the spacing of primes but I also wondered if the spacing pattern might be very, very long and we haven't reached the end yet.

Has someone "proved" that a pattern will never occur?

Is anyone actually analyzing the spacing?

Thanks again.
____________
https://signature.statseb.fr/sig-2259.png

Profile Herr RoedyProject donor
Avatar
Send message
Joined: 2 Jan 13
Posts: 26
ID: 187570
Credit: 35,835,774
RAC: 0
321 LLR Silver: Earned 100,000 credits (207,050)Cullen LLR Silver: Earned 100,000 credits (160,835)ESP LLR Silver: Earned 100,000 credits (124,931)PPS LLR Amethyst: Earned 1,000,000 credits (1,659,845)PSP LLR Silver: Earned 100,000 credits (103,698)SoB LLR Silver: Earned 100,000 credits (254,594)SR5 LLR Silver: Earned 100,000 credits (119,821)SGS LLR Silver: Earned 100,000 credits (390,992)TRP LLR Silver: Earned 100,000 credits (186,250)Woodall LLR Silver: Earned 100,000 credits (148,088)PPS Sieve Sapphire: Earned 20,000,000 credits (30,504,179)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Silver: Earned 100,000 credits (442,172)TRP Sieve (suspended) Gold: Earned 500,000 credits (855,922)GFN Gold: Earned 500,000 credits (677,397)
Message 66219 - Posted: 31 May 2013 | 9:15:41 UTC

Well, recently a pattern has been proven:
The gap between 2 prime numbers is never greater than 70 million. Truly remarkable, considering how numbers can get infinitly large.

Btw, if you're into real hardcore research, try using google scholar. You can get acces to a lot of scientific papers and if you're a student you can probably acces the full version of all papers for free.
____________
In the hood then the ladies saying "Roedy you hot"
They like me, I want them to love me like they love 'Pac

Profile pschoeferProject donor
Volunteer developer
Volunteer tester
Avatar
Send message
Joined: 20 Sep 05
Posts: 668
ID: 845
Credit: 2,380,524,848
RAC: 16,367
Found 2 primes in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 2 primes in the 2020 Tour de PrimesFound 1 prime in the 2020 Tour de Primes Mountain StageFound 2 primes in the 2021 Tour de Primes321 LLR Turquoise: Earned 5,000,000 credits (7,917,282)Cullen LLR Turquoise: Earned 5,000,000 credits (9,669,460)ESP LLR Jade: Earned 10,000,000 credits (15,505,816)Generalized Cullen/Woodall LLR Sapphire: Earned 20,000,000 credits (20,214,657)PPS LLR Sapphire: Earned 20,000,000 credits (20,587,796)PSP LLR Jade: Earned 10,000,000 credits (12,427,826)SoB LLR Jade: Earned 10,000,000 credits (15,175,194)SR5 LLR Sapphire: Earned 20,000,000 credits (23,096,513)SGS LLR Turquoise: Earned 5,000,000 credits (7,821,456)TPS LLR (retired) Bronze: Earned 10,000 credits (76,372)TRP LLR Jade: Earned 10,000,000 credits (16,773,842)Woodall LLR Turquoise: Earned 5,000,000 credits (8,519,621)321 Sieve (suspended) Jade: Earned 10,000,000 credits (11,111,528)Cullen/Woodall Sieve (suspended) Sapphire: Earned 20,000,000 credits (20,000,264)Generalized Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (11,111,347)PPS Sieve Double Silver: Earned 200,000,000 credits (460,091,000)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Ruby: Earned 2,000,000 credits (3,177,104)TRP Sieve (suspended) Turquoise: Earned 5,000,000 credits (5,556,644)AP 26/27 Double Bronze: Earned 100,000,000 credits (140,570,947)GFN Double Silver: Earned 200,000,000 credits (435,336,887)WW Emerald: Earned 50,000,000 credits (55,920,000)PSA Double Amethyst: Earned 1,000,000,000 credits (1,079,860,880)
Message 66220 - Posted: 31 May 2013 | 9:47:34 UTC - in response to Message 66219.

Well, recently a pattern has been proven:
The gap between 2 prime numbers is never greater than 70 million. Truly remarkable, considering how numbers can get infinitly large.

Zhang did not prove that the gap is < 70M for every pair of consecutive primes, but just that there are infinitely many such pairs. It's still possible (and in fact quite likely) that there are gaps > 70M.
____________

Profile sergeProject donor
Avatar
Send message
Joined: 21 Jun 12
Posts: 112
ID: 144858
Credit: 263,964,983
RAC: 98,529
Discovered 1 mega primeEliminated 2 conjecture "k"s321 LLR Turquoise: Earned 5,000,000 credits (5,342,838)Cullen LLR Silver: Earned 100,000 credits (158,983)ESP LLR Gold: Earned 500,000 credits (505,527)Generalized Cullen/Woodall LLR Ruby: Earned 2,000,000 credits (2,268,642)PPS LLR Sapphire: Earned 20,000,000 credits (49,956,379)PSP LLR Silver: Earned 100,000 credits (120,541)SoB LLR Amethyst: Earned 1,000,000 credits (1,280,028)SR5 LLR Ruby: Earned 2,000,000 credits (2,649,390)SGS LLR Gold: Earned 500,000 credits (518,356)TRP LLR Silver: Earned 100,000 credits (141,131)Woodall LLR Silver: Earned 100,000 credits (116,405)Cullen/Woodall Sieve (suspended) Silver: Earned 100,000 credits (235,088)PPS Sieve Amethyst: Earned 1,000,000 credits (1,031,526)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (500,445)TRP Sieve (suspended) Gold: Earned 500,000 credits (507,938)AP 26/27 Turquoise: Earned 5,000,000 credits (5,078,008)GFN Double Bronze: Earned 100,000,000 credits (191,259,664)WW Ruby: Earned 2,000,000 credits (2,004,000)PSA Silver: Earned 100,000 credits (291,533)
Message 66234 - Posted: 1 Jun 2013 | 1:39:58 UTC - in response to Message 66220.
Last modified: 1 Jun 2013 | 1:40:39 UTC

Not just quite likely but definitely exist and easily constructed.
Consider all numbers 70000002!+k with 2<=k<=70000002. All composite.

Profile ~~~(,__,)^'>Project donor
Volunteer tester
Avatar
Send message
Joined: 30 Jan 08
Posts: 3731
ID: 18322
Credit: 49,385,163
RAC: 0
321 LLR Gold: Earned 500,000 credits (550,585)Cullen LLR Gold: Earned 500,000 credits (668,541)ESP LLR Silver: Earned 100,000 credits (193,409)PPS LLR Ruby: Earned 2,000,000 credits (3,796,320)PSP LLR Gold: Earned 500,000 credits (521,137)SoB LLR Gold: Earned 500,000 credits (534,235)SR5 LLR Gold: Earned 500,000 credits (741,726)SGS LLR Amethyst: Earned 1,000,000 credits (1,044,407)TRP LLR Silver: Earned 100,000 credits (270,664)Woodall LLR Silver: Earned 100,000 credits (162,233)321 Sieve (suspended) Bronze: Earned 10,000 credits (32,623)Cullen/Woodall Sieve (suspended) Jade: Earned 10,000,000 credits (10,307,669)PPS Sieve Sapphire: Earned 20,000,000 credits (22,766,584)Sierpinski (ESP/PSP/SoB) Sieve (suspended) Gold: Earned 500,000 credits (620,950)TRP Sieve (suspended) Amethyst: Earned 1,000,000 credits (1,002,904)AP 26/27 Silver: Earned 100,000 credits (171,036)GFN Turquoise: Earned 5,000,000 credits (5,319,121)PSA Gold: Earned 500,000 credits (675,622)
Message 66247 - Posted: 1 Jun 2013 | 14:20:40 UTC - in response to Message 65981.

...
I assumed from the start that there was no "known" pattern to the spacing of primes but I also wondered if the spacing pattern might be very, very long and we haven't reached the end yet...


I've noticed a pattern. Prime numbers never end in 4 , 6, 8 or 0 and hardly ever end in 2 or 5.


____________
Oh Bondage? Up Yours.

http://www.youtube.com/watch?v=ogypBUCb7DA

Profile Crun-chiProject donor
Volunteer tester
Avatar
Send message
Joined: 25 Nov 09
Posts: 3070
ID: 50683
Credit: 63,378,402
RAC: 268
Eliminated 1 conjecture "k"Found 1 prime in the 2018 Tour de PrimesFound 1 prime in the 2019 Tour de PrimesFound 1 prime in the 2020 Tour de PrimesFound 1 prime in the 2021 Tour de Primes321 LLR Silver: Earned 100,000 credits (229,492)Cullen LLR Silver: Earned 100,000 credits (110,733)PPS LLR Jade: Earned 10,000,000 credits (11,335,374)PSP LLR Silver: Earned 100,000 credits (104,385)SoB LLR Silver: Earned 100,000 credits (106,117)SR5 LLR Silver: Earned 100,000 credits (139,802)SGS LLR Amethyst: Earned 1,000,000 credits (1,325,207)TRP LLR Gold: Earned 500,000 credits (626,755)Woodall LLR Silver: Earned 100,000 credits (122,944)321 Sieve (suspended) Silver: Earned 100,000 credits (104,900)Cullen/Woodall Sieve (suspended) Ruby: Earned 2,000,000 credits (2,000,599)Generalized Cullen/Woodall Sieve (suspended) Gold: Earned 500,000 credits (515,556)PPS Sieve Jade: Earned 10,000,000 credits (11,872,830)TRP Sieve (suspended) Silver: Earned 100,000 credits (255,612)AP 26/27 Ruby: Earned 2,000,000 credits (2,583,960)GFN Sapphire: Earned 20,000,000 credits (23,334,026)WW Amethyst: Earned 1,000,000 credits (1,088,000)PSA Turquoise: Earned 5,000,000 credits (7,522,050)
Message 66274 - Posted: 2 Jun 2013 | 7:17:48 UTC - in response to Message 66247.

wrong answer :-)
some numbers always end with those numbers :-)
____________
92*10^1439761-1 NEAR-REPDIGIT PRIME :) :) :)
4 * 650^498101-1 CRUS PRIME
314187728^131072+1 GENERALIZED FERMAT
Proud member of team Aggie The Pew. Go Aggie!

Message boards : General discussion : Is there a pattern to prime numbers?

[Return to PrimeGrid main page]
DNS Powered by DNSEXIT.COM
Copyright © 2005 - 2021 Rytis Slatkevičius (contact) and PrimeGrid community. Server load 4.80, 2.72, 2.10
Generated 21 Sep 2021 | 21:15:25 UTC