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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 AP
about a year ago and posted his announcements to both
Primes-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 ]
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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
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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
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Current record [ May 10, 2001 ] see WONplate 99
More on palindromic primes...
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