WON plate91 | World!OfNumbers Primefree Palindrome Interval [ February 22, 2001 ] 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! A000091 Prime Curios! Prime Puzzle Wikipedia 91 Le Nombre 91 Numberland 91
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