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Such number is called "a delayed palindrome". It is not known whether all non-palindromic numbers can be paired with palindromic numbers in this way. While no number has been proven to be unpaired, many do not appear to be. For example, 196 does not yield a palindrome even after 700,000,000 iterations.
Except for 11, all palindromic primes have an odd number of digits, because the divisibility test for 11 tells us that every palindromic number with an even number of digits is a multiple of 11. It is not known if there are infinitely many palindromic primes in base 10.
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]
Symbol of Belphegor's prime, represented by the Greek letter π upside down. Belphegor's prime is the palindromic prime number 1 000 000 000 000 066 600 000 000 000 001 (10 30 + 666 × 10 14 + 1), a number which reads the same both backwards and forwards and is only divisible by itself and one.
The thread does not include the original seed or kin number, but only the numbers that are common to both, after they converge. Seed numbers are a subset of Lychrel numbers, that is the smallest number of each non palindrome producing thread. A seed number may be a palindrome itself. The first three examples are shown in bold in the list above.
A radar serial number reads the same backwards and forwards, like a palindrome. For example, 06288260. A good condition, uncirculated $1 radar could sell for about $25 — or even more than $100.
This year's high holiday will be extra trippy. April 20, known colloquially as 420 or a holiday for marijuana enthusiasts, falls on April 20, 2024, this year, or 4/20/2024, making it a palindrome ...
Since the palindrome at the MirroredCenter is "aba" and extends beyond the boundaries of the "Old" palindrome, we know the longest palindrome at the second "b" can only extend up to the border of the "Old" palindrome. We know this because if the character after the "Old" palindrome had been an "a" instead of a "c", the "Old" palindrome would ...