THE NINE AND TEN PRIMES PROJECT
(The amazing story of the discovery of
nine and finally ten consecutive primes in arithmetic progression)
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:
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