World!OfNumbers |
WON plate 214 | |
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[ thus building larger and larger numbers. With each palindrome added to the chain we check for its primeness or pseudoprimeness. For the ascending case I soon discovered manually these two nice primes !
123456789112233445566 Is this a rare and lonely couple 77 and 101 ? This is how I tackle the topic. I use Pari/gp { cnt=0; x=[]; for(i=1,10000000, p=digits(i);marque=0;ld=p[length(p)]; if(Vecrev(p)==p, x=concat(x,p); cnt+=1; marque=1; ); if((ld==1||ld==3||ld==7||ld==9)&&marque==1, print(cnt," ",i); write("C:/pari/Smpal.txt", fromdigits(x)); ); ); } its status between composite and 3-PRP! Pari/gp also has a function 'ispseudoprime()' but is very slow with large numbers.
pfgw64 "C:\pari\Smpal.txt"
and finally check the logfile ('pfgw.log') for any (pseudo)primes. For the descending case I soon discovered manually these three nice primes !
This looks like a nice but isolated (?) trio 131 , 494 and 747 . Here is the program with adaptations for the descending case. { cnt=0; x=[]; for(i=1,10000000, p=digits(i);marque=0; if(Vecrev(p)==p, x=concat(p,x); cnt+=1; marque=1; ); if(marque==1, print(cnt," ",i); write("C:/pari/Rsmpal.txt", fromdigits(x));); ); }
pfgw64 "C:\pari\Rsmpal.txt"
You only need to check now the logfile ('pfgw.log') for any results. And the program already delivers! The fourth number is 82328 .
Lastly there is the combined case of ascending towards Let us call these palindromes Palindache Numbers . Here we are dealing with Palindromic (pseudo)Primes | |||

A000214 Prime Curios! Prime Puzzle Wikipedia 214 Le nombre 214 |

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