## Thursday, November 18, 2021

### Pandigital palindromic sums

Two days ago Éric Angelini posted on MathFun:

234567898765432 + 1000000000000000 = 1234567898765432

... noting that (ignoring the arithmetic symbols) the concatenated 47 digits are a palindrome. Éric wondered about smaller palindromic sums where all ten digits are present ("pandigital" in the sense of A171102). Here are the 24 smallest:

12076 + 38354945 = 38367021
12076 + 83854945 = 83867021
12376 + 80854945 = 80867321
12876 + 30354945 = 30367821
13086 + 27254945 = 27268031
13086 + 72754945 = 72768031
13286 + 70754945 = 70768231
13786 + 20254945 = 20268731
21067 + 38354945 = 38376012
21067 + 83854945 = 83876012
21367 + 80854945 = 80876312
21867 + 30354945 = 30376812
23087 + 16154945 = 16178032
23087 + 61654945 = 61678032
23187 + 60654945 = 60678132
23687 + 10154945 = 10178632
31068 + 27254945 = 27286013
31068 + 72754945 = 72786013
31268 + 70754945 = 70786213
31768 + 20254945 = 20286713
32078 + 16154945 = 16187023
32078 + 61654945 = 61687023
32178 + 60654945 = 60687123
32678 + 10154945 = 10187623

## Thursday, November 11, 2021

### What a difference five months make

Five months ago, I showcased the then-ten-largest-known Leyland primes. Here's an update:

500973  (100207,99856)   Gabor Levai          Nov 2021
500702  (100263,98600)   Gabor Levai          Sep 2021
386642   (81650,54369)   Yusuf AttarBashi     Jun 2021
386561   (80565,62824)   Hans Havermann       Aug 2021
386548   (83747,41272)   Hans Havermann       Aug 2021
386434  (328574,15)      Sergey Batalov       May 2014
302858   (84181,3960)    Hans Havermann       Nov 2021
301815   (83278,4209)    Hans Havermann       Sep 2021
301763   (64431,48250)   Hans Havermann       Sep 2021
301716   (67237,30714)   Hans Havermann       Sep 2021

The first column gives the number of decimal digits. The Leyland number of an (x,y) pair is x^y + y^x. Nine of these ten entries are new. Of course my list of all known Leyland primes is always up-to-date.