Two Palindromic Prime Records
by Harvey Dubner (email) [ January 25, 2001 ]
First, I found a set of three 1001digit 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 AP about a year ago and posted his announcements to both PrimesL and PrimeForm mailing lists [February 9, 2000]. It's still available at http://groups.yahoo.com/group/primeform/message/511 Communicated by Warut (email) dd. [January 26, 2001]

Harvey's rediscovery was found after about a 10 hour search on a Pentium III/400.
Since then, after about 10 more computerdays 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*10^{496} = 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 7set 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...