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Message: <blockquote data-quote="Novindu" data-source="post: 17394" data-attributes="member: 718">While we're on the subject of numbers closely related to 666...in July 2000 I snapped the following picture of my car's odometer<img src="http://img140.imageshack.us/img140/1007/odoce0.jpg" alt="" class="fr-fic fr-dii fr-draggable " style="" />which suggests that it might be worthwile to explore the double-wide-beast number (666666). Besides the obvious 666666 = 1001 x 666, Patrick De Geest points out that 666666 is a palindrome in both base 10 and base 16 (hex-adecimal - get it?), where its value is A2C2A. He also notes that in base 31 it is MBMB, which just like 666666 (made of two 666's) is formed by concatenating two identical parts (MB). Perhaps MB could be read as Multiple Beast.[found by Jud McCranie] It is a theorem that every positive integer occurs as the period length of the reciprocal of some prime. So, the obvious question arises: what's the smallest prime with period length 666? The answer was found in June 1998:p = 902659997773 is the smallest prime whose reciprocal has period length 666.The first 666 digits after the decimal point of 1/p (which then repeat) are:000000000001107836840523732794015856393629176199911567364459553453849096605279881838076680979988886781773038423114524370500571392445408560228574284480352437836776725525116619485115892576776519141738094220028289530945207260114524370499463555604884827434558428086723261636865158160657066031266795971496637303661413240039402749172168836999999999998892163159476267205984143606370823800088432635540446546150903394720118161923319020011113218226961576885475629499428607554591439771425715519647562163223274474883380514884107423223480858261905779971710469054792739885475629500536444395115172565441571913276738363134841839342933968733204028503362696338586759960597250827831163Observe that if you turn the prime p upside down, there's a 666 inside, slightly to the left of the middle, and if you turn the single period of 1/p upside down, there's a 66666666666 inside, slightly to the left of the middle![from Simon Whitechapel] A mathematically important number sequence is:7, 17, 19, 23, 29, 47, 59, 61, 97, 109, 113, 131, 149, ...which is the sequence of primes p whose reciprocal in base 10 has maximum period p-1. The last one, 1/149 with period 148, has the following digits after the decimal point (which then repeat):0067114093959731543624161073825503355704697986577181208053691275167785234899328859060402684563758389261744966442953020134228187919463087248322147651As luck would have it, the sum of these is 666. If these 148 numbers (the first 148 digits of 1/149) are written as the top row of a 148x148 square grid, and then the digits of 2/149 as the second row, then 3/149 and so on, the result is a 148x148 pseudo-magic square, in which every row and column sums to 666.[sent in by P. De Geest] The smallest prime number with a gap of 666 (that is, such that the prime following it is larger than it by exactly 666) is18691113008663Note the three sixes!  Also, Patrick Capelle points out that this prime (1869113008663) and the following one (1869113008663 + 666 = 18691113009329) both have the same digit sum, 53 (also a prime).Define a dottable fraction as one in which dots (representing multiplication) can be interspersed in both the numerator and denominator to produce an expression that's equal to the original fraction. The noteworthy dottable fraction 666   =   6·6·6  64676     6·46·76 has a numerator of 666 and a denominator of the form 6x6y6.Here's another one (actually, two) based on a fraction [by Manley Perkel and Mike Keith].  The fraction 1666/6664 (which has a 666 in both numerator and denominator) has two interesting properties:(1) The numerical value of the fraction (0.25) is the same as the numerical value of the fraction you get by "canceling" (i.e., erasing or removing) the 666 from both the numerator and denominator.(2) The value of the fraction is the same as the value you get by splitting the fraction in half and multiplying the two parts together; that is,1666  =  16 . 666664     66   64A fraction like this is known as a fractured fraction.The alphametic below has a unique solution (i.e., there is only one way to replace letters with digits so that the addition sum is correct):   SIX   SIX   SIX+BEAST SATAN[by Monte Zerger] Note that 1998 (a recent year) = 666 + 666 + 666. Not only that, but if we set A=3, B=6, C=9, etc., we find, amazingly, thatNINETEEN NINETY EIGHT = 666Frank Fiederer points out that the age of the United States in 1998 is also related to 666, since1998 - 1776 = 666/3.Finally, we close with an observation that makes a commentary on the folly of attaching a specific meaning to the number 666. If the letter A is defined to be equal to 36 (=6·6), B=37, C=38, and so on, then: The sum of the letters in the word SUPERSTITIOUS is 666.</blockquote>

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