[ May 10, 2001 ]
Palindromic Primes in Arithmetic Progression
Harvey Dubner (†) (email)
Taking advantage of faster computers, Harvey Dubner found three palindromic primes
of 2001-digits in arithmetic progression. The search method consisted of finding
palindromic probable primes of 2001 digits of the form,
1000000...000000K000000...0000001, where K is a palindrome.
Sequential values of K are tested so that the list of probable primes increase
monotonically. Periodically the list is examined to see if any arithmetic progressions
exist. A set of three appeared after 180 prp's were found.
The search time was about 20 computer-days of 500 MHz cpu.
The three prp's were then easily certified as being true primes.
3 titanic palindromic primes (palprimes)
in arithmetic progression
pp1 = 1000...00053298389235000...0001 2001 digits|
pp2 = 1000...00053395459335000...0001
pp3 = 1000...00053492529435000...0001
97070100000...0000 = common difference
Harvey thinks these are the largest such set that is known.
If you are aware of a larger set please let us know.
Previous such record WONplate 90
More on palindromic primes...