[ *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...