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[ January 25, 2001 ]
Two Palindromic Prime Records
Harvey Dubner (email)

First, I found a set of three 1001-digit palprimes in arithmetic progression.
As far as I know, this is the only such titanic set that is known.

 Warut Roonguthai found this set of 3 titanic palindromic primes in APabout a year ago and posted his announcements to bothPrimes-L and PrimeForm mailing lists [ February 9, 2000 ].It was available at http://groups.yahoo.com/group/primeform/message/511 Communicated by Warut (email) dd. [ January 26, 2001 ]

Harvey's re-discovery was found after about a 10 hour search on a Pentium III/400.
Since then, after about 10 more computer-days no other set was found.

3 titanic palindromic primes (palprimes)
in arithmetic progression

 pp1 = 1000...00013186668131000...0001    1001 digits pp2 = 1000...00014266666241000...0001 pp3 = 1000...00015346664351000...0001                  107999811*10496 = common difference pp1 = 10^1000 + X*10^495 + 1 pp2 = pp1 + d*10^496 pp3 = pp2 + 2*d*10^496 X = 13186668131 d =   107999811

Second, it occurred to me that while there have been investigations
of palprimes in arithmetic progression I knew of no work on consecutive
palprimes in arithmetic progression. I started an exhaustive search
and rapidly found 3, 4, 5 consecutive palprimes in AP. 6 took longer
but the smallest such set finally appeared. It is shown below.
Several other sets have also been found. So far, no 7-set has been
found, and it may be that an exhaustive search for 7 may not be appropriate.

6 consecutive palindromic primes (palprimes)
in arithmetic progression

 1981856124216581891 1981856135316581891 1981856146416581891 1981856157516581891 1981856168616581891 1981856179716581891         11100000000 = common difference

Current record [ May 10, 2001 ] see WONplate 99
More on palindromic primes...

A000090 Prime Curios! Prime Puzzle
Wikipedia 90 Le Nombre 90 Numberland 90
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