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Title: Math/Number Theory/Prime Numbers - The Nine and Ten Primes Project The discovery of nine and finally ten consecutive primes in arithmetic progression.
Notes_and_Literature_on_Prime_Numbers With applets to demonstrate properties of primes.

Number_Spiral Explains this method of visually representing the distribution of primes and the relationships between factors and products.

On-Line_Encyclopedia_of_Integer_Sequences_(OEIS)__Primes Index to information about many integer sequences involving primes. Site includes numerous other prime-related sequences.

Patterns_in_Primes Examples of mostly digit patterns collected by Harvey Heinz.

Primality Introductory text on the theory of prime numbers and number fields. Contains proofs of some important theorems including the fundamental theorem of arithmetic. [PDF]

Primality_Testing_with_Fermat\'s_Little_Theorem Test numbers for primality and pseudoprimality in Java.


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The Search for Nine and Ten Consecutive Primes in Arithmetic Progression

THE NINE AND TEN PRIMES PROJECT

(The amazing story of the discovery of nine and finally ten consecutive primes in arithmetic progression)

Background

Search for nine consecutive primes in arithmetic progression

Progress The Result The official announcement on the NMBRTHRY-Server, 1998 January 24 To see the nine 92-digit primes click here Further Information The following newsletters chart the progress of the Nine Primes project: 9prNL01, 9prNL02, 9prNL03, 9prNL04, 9prNL05, 9prNL06. References: Ivars Peterson' s articles Nine Primes in a Row , ScienceNewsOnline-MathTrek, 1998 February 7 and Nine Primes in a Row , MAA-Online (The Mathematical Association of America), 1998 February 9. Keith Devlin' s report The number of the beast , The Guardian, 1998 February 19.

Search for ten consecutive primes in arithmetic progression

The Result The official announcement on the NMBRTHRY-Server, 1998 March 8 To see the ten 93-digit primes click here To see the pictorial representation click here Further Information The following newsletters chart the progress of the Ten Primes project: 10prNL1, 10prNL2, 10prNL3 References: Keith Devlin' s article Prime time (10) , The Guardian, 1998 March 19. Ivars Peterson' s articles A Prime Surprise , ScienceNewsOnline-MathTrek, 1998 March 21 and A Prime Surprise , MAA-Online (The Mathematical Association of America), 1998 March 23. Paul Zimmermann' s article Ten Consecutive Primes in Arithmetic Progression , mathPAD Vol8No1, p30-32 , March 1998. Eric W. Weisstein' s Prime Arithmetic Progression , World of Mathematics , April 1998. Sloane' s A033290 , The On-Line Encyclopedia of Integer Sequences, April 1998 Chris K. Caldwell, Consecutive Primes in Arithmetic Progression , The top twenty Ten Consecutive Primes in Arithmetic Progression , Mathematics of Computation (2002, Vol. 71, No. 239, pages 1323-1328)

Eleven Primes ?

Harvey Dubner says: "Eleven primes is another ball game entirely. It would take at least [a trillion] times longer to solve than 10 primes." Paul Zimmermann says: This is in fact much harder. The reason is that, up to ten primes, one can have a common difference of 210 between primes, whereas for eleven primes, the common difference must be at least 2310. The optimal size of the primes to search for is then about 600 digits instead of 90 digits for 7 to 10 primes. As a consequence, the expected search time is about 10^13 times larger than for 10 primes! Of course, this is only an estimation on average. It does not prevent lucky people like Manfred Toplic to find a 11-primes record in a few weeks! And Tony Forbes says: "When we do find the 10 primes, we expect the record to stand for a very long time to come."

Other Comments ...

Prof. Dr. Paulo Ribenboim (Author of *The New Book of Prime Number Records*): "Due to your great luck --- not counting the work --- you may abstain from buying lottery tickets for a while." Luther Welsh (Discoverer of the 29th Mersenne Prime - 1988): .... I suppose you will be the first person to find 11 Consecutive Mersenne Primes? .... Last Updated on 2004 March 7, by Manfred Toplic var data, p; var agt=navigator.userAgent.toLowerCase(); p='http'; if((location.href.substr(0,6)=='https:')||(location.href.substr(0,6)=='HTTPS:')) {p='https';} data = '&r=' + escape(document.referrer) + '&n=' + escape(navigator.userAgent) + '&p=' + escape(navigator.userAgent) if(navigator.userAgent.substring(0,1)>'3') {data = data + '&sd=' + screen.colorDepth + '&sw=' + escape(screen.width+ 'x'+screen.height)}; document.write(''); document.write(' ');
 

The

discovery

of

nine

and

finally

ten

consecutive

primes

in

arithmetic

progression.

http://members.aon.at/toplicm/cp09.html

The Nine and Ten Primes Project 2008 November

dvd rental

dvd


The discovery of nine and finally ten consecutive primes in arithmetic progression.

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