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

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