December 21 2012 possesses cryptic prime properties Aziz

December 21, 2012 possesses “cryptic” prime properties Aziz S. Inan, Ph. D. Professor, Electrical Engineering University of Portland, Oregon December 21, 2012 1

Last day of Long Count Mayan Calendar-December 21, 2012 • There is general consensus that the 13 baktun* Long Count Mayan Calendar cycle will end on December 21, 2012 • Unlike all the hoax stories however, I don’t believe that the world will come to an end on December 21, 2012 (or any other day in 2012) *A baktun is a period of 144, 000 days (about 393 years) in the Long Count, so, 13 baktuns is 1, 872, 000 days December 21, 2012 2

December 21, 2012 has special “cryptic” numerical properties • In addition to being the last day of the Long Count Mayan Calendar cycle, December 21, 2012 is also unique because its date number possesses special “cryptic” numerical properties • The goal of this presentation is to reveal these cryptic numerical properties to help change the image of this day from being a “dark, mysterious” day to a “fun, brainteasers” day December 21, 2012 3

December st 21 in a leap year • December 21 st is the 356 th day of each 366 day leap year such as 2012 • Therefore, these two numbers (356 and 366) together can be viewed as representing December 21 st in each leap year • Interestingly enough, numbers 356 and 366 together are also cryptically connected to December 21 st, 2012, how? December 21, 2012 4

December st 21 in a leap year • First, reverse number 356 to obtain 653 • Then, take numbers 366 and 653 and put them side by side as 366653 • Note that number 366653 still cryptically represents December 21 st in a leap year • Surprisingly, this year’s December 21 st can be cryptically derived from number 366653 in two different ways December 21, 2012 5

The 366653 rd prime number cryptically leads to 21 -12 -2012! • First, the 366653 rd prime number happens to be 5280503 • Also, note that each leap year is divisible by four • Amazingly, four times 5280503 equals 21122012, the single full date of December 21, 2012 expressed in the day-month-year date format! Wow! December 21, 2012 6

Prime 356663 also cryptically yields 21 -12 -2012! • • • Next, reverse of number 366653 is 356663 Number 356663 is the 30500 th prime number In addition, 30500 = 305 x 100 Note that four times reverse of 305 yields 2012! Number 2012 plus 100 gives 2112! Finally, numbers 2112 and 2012 put side by side lead to 21122012! Fascinating! December 21, 2012 7

Numbers 356 and 663 also cryptically produce 21122012! • This cryptic connection is a bit of a stretch but it is also fun • Remember the two numbers 356 and 366, representing December 21 st in a leap year? • The difference of 356 and the reverse of 366 is 307 • Interestingly enough, 307 can be viewed as 305 + 2 • Twice the product of the reverses of 305 and 2 equals 2012! December 21, 2012 8

Numbers 356 and 663 also cryptically produce 21122012! • Next, numbers 305 and 2 side by side make 3052 • The prime factors of 3052 are 2, 7, and 109 • Interestingly enough, 2012 + 109 – 2 – 7 = 2112! • Again, 2112 and 2012 put side by side is 21122012! Isn’t this something? December 21, 2012 9

December 21 st in 2112 will be very special • As an aside, 100 years later, December 21 st in palindrome year 2112 will be a very special calendar date, why? • The single full date of December 21 st, 2112 will be 2112, an eight-digit palindrome date to occur in a palindrome year! • The last such date occurred on February 20, 2002, expressed as 2002 and no other such date is to occur in this millennium December 21, 2012 10

References 1. A. S. Inan, “Numerical Oddities of December 21, 2012—Ending Date of the Long Mayan Calendar, ” December 21, 2011 https: //faculty. up. edu/ainan/Mayan. Long. Count. E nds 21 December 2012. pdf 2. Big Primes: Large list of prime numbers http: //www. bigprimes. net/ December 21, 2012 11