or 666 x 64 = 42624 another nice palindrome...
Featured in Prime Curios! 9230329
Another beautiful palprime by G. L. Honaker, Jr. [ March 13, 1999 ]
Using his own terminology we call this a Pi-lindromic prime !
This -lindromic prime has 53 digits. [Sloane's reference A039954 and A119351.]
Featured in Prime Curios! 31415...51413 (53-digits)
A smoothly undulating palindromic prime (SUPP) containing 15 digits. [ March 10, 1999 ]
Hmmm... the smallest 'mnemonic' prime ?
Featured in Prime Curios! 151515151515151
A 175-digit tetradic palprime discovered by G. L. Honaker, Jr. on [ March 9, 1999 ]
Featured in Prime Curios! 10080...08001 (175-digits)
The smallest(?) palprime of length 313 starting and ending with 313. [ March 7, 1999 ]
Note that both 313 and 1183811 are palindromic reflectable primes - a Sloane A007616 class !
Clearly G. L. Honaker, Jr. is fascinated with triadic (or 3-way) primes i.e. which are invariant upon
reflection only along the line they are written on, so the digits may be 0, 1, 3 and 8.
Featured in Prime Curios! 31300...00313 (313-digits)
A palprime with a palprime total of digits namely 101 this time ! [ March 6, 1999 ]
A nice palprime of length 59 sent by G. L. Honaker, Jr. on [ February 28, 1999 ]
See the section 'Enoch Haga' for the story behind the mysterious number 313 at page .
And yes we all know that 666 is the famous number of the beast...
About 'Descriptive Primes'
The following find of G. L. Honaker, Jr. is a by-product of his sequence A036978 dd. [ January 17, 1999 ].373 palprime
311331173113 final prime of length 12.
Start with a prime (that happens to be palindromic in this case) e.g. 373.
Featured in Prime Curios! 373
Each next term describes the previous terms according to the rules stipulated in A005150.
The puzzle statement is now to find the largest series of primes.
Our example is the only 3-digit number (a palprime at that!) producing 3 more primes in a row !
"There may be better 'generators' out there... this is as far as I have taken it." G. L. Honaker, Jr. wrote.
Carlos Rivera saw this puzzle on 'descriptive primes' and went also to work - See Puzzle 36.233 prime
11122122132113 final prime of length 14.
He reported to me [ January 22, 1999 ] that he found a series of six (6) terms that are primes.
[ See Sloane A037033 - A038131 - A038132 ]
Featured in Prime Curios! 233
This one sent in by Carlos the day after [ January 23, 1999 ]120777781 prime
31131122211211131221101321141321171113122118312211 final prime is 50 digits long!
Later on [ January 24, 1999 ] Carlos found yet another generator yielding a prime of 52 digits still as a sixth term.402266411 prime
1113122114111312211031133112132116111312211413112221 final prime
Mike Keith has found three more length-6 prime chains [ February, 1999 ]
Here are the beauties !
starting at prime 1171465511 and ending with a 54-digit prime :21171114162521 prime 2
1221173114111612151211 prime 3
11222117132114311611121115111221 prime 4
21322117111312211413211631123115312211 prime 5
121113222117311311222114111312211613211213211513112221 final prime 6
starting at prime 1623379207 and ending with a 74-digit prime :111612231719121017 prime 2
311611221311171119111211101117 prime 3
1321162122111331173119311231103117 prime 4
111312211612112231232117132119132112132110132117 prime 5
31131122211611122122131112131221171113122119111312211211131221101113122117 final prime 6
starting at prime 1955771683 but ending with a smaller 68-digit prime :1119252711161813 prime 2
311912151217311611181113 prime 3
132119111211151112111713211631183113 prime 4
111312211931123115311231171113122116132118132113 prime 5
31131122211913211213211513211213211731131122211611131221181113122113 final prime 6
Mike Keith predicts a length-7 chain should occur around 10^11, after having made some calculations
about the relative probability to find chains of this type of different length.
[ November 2002 ]
This is not the end of the story ! An exhaustive search was done by Walter Schneider.
Currently the search has arrived at starting number 10^11. In total 59 sequences of
length 6 are found and one sequence of length 7 starting at 19972667609.
So far no sequence of length 8 or more is known.
Carlos Rivera (email) from Nuevo León, México and Jaime Ayala (email) - go to topic
Enoch Haga (email) for his discoveries of palindromes in the 37th Mersenne prime - go to topic
G. L. Honaker, Jr. (email) from Bristol, Virginia made a beastly interesting discovery - go to topic
Mike Keith (email) found many of the larger self-descriptive primes- go to topic
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