[ September 10, 2022 ]
Invitation for factorizing Smoothly Undulating Palindromes (SUP's)
and finding ever larger Near Smoothly Undulating Primes (NSUP's)
Patrick De Geest

1

A while ago I started a factorization project based on Hisanori Mishima's work
that seems to be discontinued. The intent is to find the prime factors
of all the Smoothly Undulating Palindromes (prime cases SUPP's
and by extension all composite SUP's as well).
Only a handful remain among these palindromes with less than 200 digits
that still needs factoring. An overview is available and can be reached
via this webpage Smoothly Undulating Palprimes

Feel free to participate in this project. Let me know if you are
interested and I will reserve the number for you. If this is not your
thing then maybe you know others who are dedicated number crackers.
Spread the message.

2

If the above is not your cup of tea then maybe you like to find ever larger
but very rare prime NSUP's (Near Smoothly Undulating Palindromes).
The formulae are to be found in the tables of the following pages:

undulat.htm with 2-digit undulators
Record prime so far \(\bbox[#f0f8ff,5px,border:2px solid teal]{\ (45*10^{29029}-54) \over (99*2)}\)

undulsix.htm with 6-digit undulators
Record prime so far \(\bbox[#f0f8ff,5px,border:2px solid teal]{\ (52*10^{43929}-25) \over (99*3*5^2*7)}\)

undulmore.htm with 22-digit undulators
Record prime so far \(\bbox[#f0f8ff,5px,border:2px solid teal]{\ (83*10^{48433}-38) \over (99*2*11)}\)

3

This is the odd one out.
Makoto Kamada maintains a page about the factorization of
Plateau and Depression Palindromes of the form ABB...BBA at the following address:
https://stdkmd.net/nrr/abbba.htm
He covers all possible combinations except factorization of 533...335
(because his script does not support the longer algebraic factorization (sum of 5th powers)).
Now I manually created that missing page facpdp535.htm
and anyone is invited to find missing primefactors for that list as well.