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

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,

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” day to a “fun, brainteasers” day December 21,

December 21 st 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,

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

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

Prime also cryptically yields ! Next, reverse of number is Number is the th prime number In addition, = 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 ! Fascinating! December 21,

Numbers 356 and 663 also cryptically produce ! 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 Twice the product of the reverses of 305 and 2 equals 2012! December 21,

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

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 , a palindrome date to occur in a palindrome year! The last such date occurred on February 20, 2002, expressed as and no other such date is to occur in this millennium December 21,

References 1.A. S. Inan, “Numerical Oddities of December 21, 2012—Ending Date of the Long Mayan Calendar,” December 21, nds21December2012.pdf 2. Big Primes: Large list of prime numbers December 21, 2012