[ 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 10¹⁸ ?!
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!