[ *February 22, 2001* ]

Primefree Palindrome Interval

Find an **interval** bordered by two **palindromes** starting with the same digit d

such that this **interval** contains no primes i.e., is primefree or devoid of primes.

The first seven **intervals** are :

**181 ... 191**

212 ... 222

525 ... 535

777 ... 787

787 ... 797

888 ... 898

919 ... 929

And then I had to give up, yes that soon!

Exist there a the next primefree palindrome interval ?

My own **conjecture** is that it will be very very hard to find

another **interval**. The reason is that the longer the palindromes

become the farther away two successive palindromes are,

thereby always a step ahead of having a small enough primegap.

E.g. **1234321** and **1235321**

differ by __1000__ but the first occurrence of a primegap of __1000__

happens only long after nl. above 10^{18} ?!

Does this conjecture hold for other bases ?

The definition stipulates that the two palindromes must start

with the same digit d, this in order to exclude the trivial solutions

like 999...1001, 9999...10001, etc.

or 29992...30003, 399993...400004, etc.

which are too easy to find of course.

The seventh **interval** **919...929** has two

palindromic prime (or palprime) borders,

just like **181...191** and **787...797** !

the only three of its kind sofar!