ID Number: A002385 (Formerly M0670 and N0247) Sequence: 2,3,5,7,11,101,131,151,181,191,313,353,373,383,727,757,787,797,919, 929,10301,10501,10601,11311,11411,12421,12721,12821,13331,13831,13931, 14341,14741,15451,15551,16061,16361,16561,16661,17471,17971,18181 Name: Palindromic primes. References A. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 228. Links: K. S. Brown, On General Palindromic Numbers P. De Geest, World!Of Palindromic Primes Keywords: nonn,base,nice,easy Offset: 1 Author(s): njas,sp
313
[ March 30, 2008 ] G. L. Honaker asked me
Did you ever see the film Catch Me If You Can (2002) ?
'313' - Enoch Haga's key to containment of the Beast !
Enoch Haga, a retired teacher (taught mathematics, computer programming and business classes for over 35 years in California public schools) - more about the author - currently living in Livermore, east of San Francisco, told me that the '313 stuff' started as an innocent challenge inspired by his friend G. L. Honaker, Jr.
Enoch likes to string this '313 stuff' together with some kind of flamboyant narrative. Now, Sri Mighty Flighty of Cattapurr, Chief Guru of California (CGC), is a convenient scapegoat for Enoch, someone on whom he canblame his mistakes. Following is his esoteric story of the containment of the beast 666 using palprime 313 !
"The other day while waiting for some PalPrimes to pop up, I happened to step outside and inhale some smog. Shortly thereafter, I received a revelation: I was told that I am controlled by Sri Mighty Flighty of Cattapurr, Chief Guru of California, and as such the SF has authorized me to issue proclamations in my name under his authority. Since Re 13:18 clearly states the number of the wild beast to be 666, and since this mark is to be placed on the forehead or on the right hand (my keyboard hand! and mouse controller!), I see that the Wild Beast, being a powerful fallen angel, is infinitely uncontained. Now the Wild Beast can only be contained by an unfallen angel, indeed one who is sent out to do battle. This, it has been revealed to be Michael, whose number is 99. The SF is content to watch them both do battle forever, and will not intervene so as to spoil the fun. Therefore, a Wild Beast, or Beast, is 666, and a Michael is 99. Each of these angels has legions of angels, b's or beasts for the Beast, and little a's or angels for Michael. 6 = beastly germ 66 = infectious germ 666 = virulent beast or the Wild Beast or B 99 = fighting angel, slayer of dragons, Michael, or M Both B and M have angels in two ranks: Michael's 1^{st} rank 9 1's x 2 or 18 (111111111666111111111) 3 3's x 2 or 18 (333666333) Michael's 2^{nd} rank 2 7's x 2 or 28 (7766677) 2 9's x 2 or 36 (9966699) DANGER! 4 x 9 = 36; this can unleash 6 more beastly germs and send them out to the four corners of the earth! Just two 3's do not contain and in fact may be sucked in by the B to gain energy! (36663 - the 3+3 adds a germ! moreover the total is now 24, and 24 / 4 = a drunken B) 5 2's x 2 = 20 (2222266622222) contains B and gives edge to M 3 4's x 2 = 24 (444666444) contains B BUT power could be leaked to B, as 24/4 = 6, and that 6 could defect from M to B Beware of 3 2's together as they may create a beastly germ! 9966699 is a double M, highly effective in containment, even better: the triple M: 999666999, and no angels can defect as 27 isn't divisible by 6! Beware of situations such as this: 6661666; notice that one of Michael's 1^{st} rank angels is vulnerable and may be captured and even eaten! It has been revealed to me that the B can be contained only through DIVISION, thus 1318/2 = 659, a PRIME (Recall Re 13:18). Thus if we divide 666/2 we obtain 333, a reduced B. Now, if we replace the middle three with an angel of the first rank, 1, we obtain 313 (the Number of the Duck), the KEY TO CONTAINMENT OF THE BEAST. 313666313 does the trick, as if there is an attack of 6 in either direction, it is immediately overwhelmed by 7 on either side. Nevertheless, the B will always keep trying! The vision fades... Sri Mighty Flighty of Cattapurr, CGC"
"The other day while waiting for some PalPrimes to pop up, I happened to step outside and inhale some smog. Shortly thereafter, I received a revelation: I was told that I am controlled by Sri Mighty Flighty of Cattapurr, Chief Guru of California, and as such the SF has authorized me to issue proclamations in my name under his authority.
Since Re 13:18 clearly states the number of the wild beast to be 666, and since this mark is to be placed on the forehead or on the right hand (my keyboard hand! and mouse controller!), I see that the Wild Beast, being a powerful fallen angel, is infinitely uncontained. Now the Wild Beast can only be contained by an unfallen angel, indeed one who is sent out to do battle. This, it has been revealed to be Michael, whose number is 99. The SF is content to watch them both do battle forever, and will not intervene so as to spoil the fun. Therefore, a Wild Beast, or Beast, is 666, and a Michael is 99. Each of these angels has legions of angels, b's or beasts for the Beast, and little a's or angels for Michael.
6 = beastly germ 66 = infectious germ 666 = virulent beast or the Wild Beast or B 99 = fighting angel, slayer of dragons, Michael, or M
Both B and M have angels in two ranks:
Michael's 1^{st} rank 9 1's x 2 or 18 (111111111666111111111) 3 3's x 2 or 18 (333666333)
Michael's 2^{nd} rank 2 7's x 2 or 28 (7766677) 2 9's x 2 or 36 (9966699) DANGER! 4 x 9 = 36; this can unleash 6 more beastly germs and send them out to the four corners of the earth! Just two 3's do not contain and in fact may be sucked in by the B to gain energy! (36663 - the 3+3 adds a germ! moreover the total is now 24, and 24 / 4 = a drunken B) 5 2's x 2 = 20 (2222266622222) contains B and gives edge to M 3 4's x 2 = 24 (444666444) contains B BUT power could be leaked to B, as 24/4 = 6, and that 6 could defect from M to B
Beware of 3 2's together as they may create a beastly germ!
9966699 is a double M, highly effective in containment, even better: the triple M: 999666999, and no angels can defect as 27 isn't divisible by 6!
Beware of situations such as this: 6661666; notice that one of Michael's 1^{st} rank angels is vulnerable and may be captured and even eaten!
It has been revealed to me that the B can be contained only through DIVISION, thus 1318/2 = 659, a PRIME (Recall Re 13:18). Thus if we divide 666/2 we obtain 333, a reduced B. Now, if we replace the middle three with an angel of the first rank, 1, we obtain 313 (the Number of the Duck), the KEY TO CONTAINMENT OF THE BEAST.
313666313 does the trick, as if there is an attack of 6 in either direction, it is immediately overwhelmed by 7 on either side. Nevertheless, the B will always keep trying!
The vision fades...
Sri Mighty Flighty of Cattapurr, CGC"
Some notes
Donald Duck ? Visited http://www.brucehamilton.com/gladstone/disneycomics/prevish.html (broken link).Now I understand why Enoch calls 313 the Number of the Duck !
"313 is the license plate number on Donald Duck's automobile!"
In the constant
The string 313 found at position 858 counting from the first digit after the decimal point. Palindrome 78387 follows immediately ! [ See also in Sloane's database sequence with index number A038101 ] The string 666 found at position 2440 counting from the first digit after the decimal point. Palprime 727 follows immediately !
The Duck Army and 313 G. L. Honaker, Jr.'s motto "QUACK ALL THAT YOU CAN QUACK!" [ February 10, 2000 ]
Interesting sources
Floating around in space for 313 days.
G. L. Honaker, Jr. reports the following fact :
The Russian astronaut Sergei Krikalev returned to Earth after spending exactly 313 days in space. In space, astronauts (or cosmonauts) can expect their heartbeat to slow and suffer from space sickness...
Websource : All Systems Go: Bar Code in Space (broken link)
A duck to the duckth.
Facts from Enoch Haga
There is only one duck in the expansion of 313^313 - a 782 digit number ! After the 406^{th} digit you'll find the one and only 313.
1274610970300263200888968784417700338335618419643837688920311024503746596164896 41249810762237495002232897811996972160699514037144492043557032105601277552468661 20534521961427863116198351965979693980604137846614187055474451810271643948594982 78737159667679625114138816298363181256549958711646379057979446259953191257493281 29013646348865942517186824182307729704748276081791721496521780740927481599977133 34136183135645205767361477983753414314622304158485220665043016109249805729529425 53755954502039432994417164077215336872224664149250572051320157903542207932768578 47789998066360064670894400346948871692058732092734190231554127965176337936104389 84279564833034071143284244326458520422902338436492705306298219928193213795513096 016308040297068762469448765341747383352706249717060033734444153
313 divides evenly any string of 312 identical digits 1, 2, 3, 4, 5, 6, 7, 8 or 9. 312 is the lowest value. There is a right triangle where the hypothenuse is 313 and the sides are 312 and 25.
"Curious and Interesting Numbers" - David Wells
The Pellian and 313
313 a Binary Gleichniszahlen-Reihe term
313 is a term from the 'Binary Gleichniszahlen-Reihe (BGR)' when converted into decimal ! Consult Sloane's sequences A045998, A045999 and A048522.
Describe after mod 2 into decimal (A045998) (A048522) ----------------------------------------------------------------------------- 1 1 1 11 11 3 21 01 1 1011 1011 11 111021 111001 57 312011 110011 51 212021 010001 17 10113011 10111011 187 1110311021 1110111001 953 3110312011 1110110011 947 3110212021 1110010001 913 3120113011 1100111011 827 2120311021 0100111001 313 ---> Number of the Duck! ...
Anno Domini 313
In 313 AD Constantine was in the 7^{th} year of his reign.
To find out what happened on any day, including March 13 (3-13) go to: Today In History
313 revisited.
Enoch Haga wrote a book "Exploring Prime Numbers on Your PC", 2nd ed. 1998, ISBN 1-885794-16-9 (3rd ed. out soon) on primes that also set off G. L. Honaker, Jr. to thinker with the palprime 313.
Beginning on page 5,
"Because 313 is my favorite number and palprime, I use it as an example to try my algorithm for testing numbers for primality. Of course 313 became my favorite number because each day when I left my teaching job, I happened to notice that the time was 3:13 pm. Usually I left home at 7:11 am because it is a double-lucky number at the craps tables! I mentioned that 313 is a palindromic number, and asked "How many palindromic primes are there? It might be fun to try to find out..."
"I'm not going to let you leave this book without learning more about my favorite number, 313. This is a three-digit palindrome whose digits sum to a lucky number, 3+1+3 =7. . . . Two of these digits, 3 and 7, are also prime, and the other isn't composite! Twice the lucky number less 1 is an unlucky number: 2*7-1=13. The digits of 14 sum to 5, another prime. The unlucky number, 13, with its digits reversed is a prime, 31, terminating a five-digit palindrome: 1 3 1 3 1. (A prime, such as 13, which is reversible to another prime, such as 31, is called an emirp.) The first digit of 313, when squared, factors the larger palindrome evenly: 13131/9 = 1459. The digits of this second factor, 1459, which is also a prime, when summed and summed again (1+4+5+9=19, and 9+1=10), give us the base of our number system, 10. To clinch it all, 313 = 12^2 + 13^2: 144 + 169 = 313, the sum of two consecutive squares. Can you discover anything else about 313 ?"
353
373
1 3 1 6 3 3 9 3 1 9 3 4 9 1 9 9 3 3 3 9 1 1 3 9 6 3 3 8 9 2 9 9 9 7 3 7 5 4 7 1 7 3 2 7 1 3 4 7 3 1 9 9 6 7 9 3 9 3 9 6 7 7 9 3
'373' the king amidst the threedigit palprimes
Let me expand with another rather small palindromic prime namely 373 . Quite uninteresting at first sight, I hear you utter. But then take another look at the following table were various random aspects of this number are displayed.You'll never say again a number is uninteresting. Mike Keith has written a very interesting paper about this uninteresting? topic.
383
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