This book is for all levels from high schools to university undergraduate level to high university graduate studies. This is a discovery based on a new invention of solving periodic numbers including prime numbers and multiple of prime numbers. The inclusion of prime numbers is very important which makes possible to deal with prime numbers totally. Luckily, Periodic Numbers are the new field in this book which leads to Recreational Mathematics. Periodic Numbers are important in this field and on all levels. It is found and discovered that all prime numbers is periodic with a specific period length. This includes all prime numbers starting from three to infinity. The digits of the period are the same for all the rational numbers of the same prime number. They have a super natural order that shifts digits from one rational numbers to the next one. This shifting of digits may vary from 1 digits, 2 digits to N-1 digits of the prime number N. This lead to a new invention discovered as cycling of periodic prime numbers (a cycle and cycling). A new Law is discovered which divides N-1 by the period length P to produce the number of cycles C. This lead to a new Computing called Periodic Computing. Multiple of prime number is also a (shifted) periodic number.
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