# Submission: A dozen mathematical oddities to celebrate Benjamin Franklin’s 312th birthday

#### Franklin is widely recognized as one of the founding fathers of the United States

Portrait of Franklin by Joseph Siffred Duplessis (ca. 1785), from Wikimedia Commons.

This month, Jan. 17, 2018 will mark Benjamin Franklin’s 312th birthday [1-3]. To remember this extraordinary man and to celebrate his 312th birthday, I constructed the following dozen mathematical oddities in his honor:

1. Franklin’s new age and his birthdate 117 (1/17) have an interesting numerical connection: three-eighths of 312 yields 117.

2. Furthermore, if Franklin’s 312th birthday is expressed as 1/17/18, the sum of 1 and 17 equals 18.

3. The prime factors of Franklin’s new age, 312, namely 2, 3, and 13, add up to 18 too.

4. Moreover, the prime factors of 11718 (1/17/18) are 2, 3, 7, and 31, which are the 1st, 2nd, 4th, and 11th prime numbers, where the sum of 1, 2, 4, and 11 also yields 18.

5. The sum of the digits of 11718 equals 18 too.

6. Also, if 1/17/18 is split as 1, 17, and 18, 1 x 17 x 18 equals 306 which is twice 153 where 153 is the Franklin number [4-6].

7. Further, the reverses of 1, 17, and 18, namely 1, 71, and 81, add up to 153.

8. Franklin’s 311th birthday last year was special too because 2017 is the 306th prime number where again, 306 equals twice 153.

9. Additionally, 2017 ends with 17, which is a number that pops up in many places in Franklin’s life [4].

10. Franklin’s 311th birthday in 2017 was also special because it followed the 226th anniversary of his death on 4/17/2016 where twice the reverse of 311, namely 113, equals 226.

11. Moreover, the sum of the digits of Franklin’s 312th birthday expressed as 1/17/2018 equals 20, the 20th prime number is 71, and three times 71 equals 213, which is the reverse of 312. Also, 71 is the reverse of 17, the frequently appearing number in Franklin’s life.

12. Lastly, if the days of year 2018 are counted backwards, that is, December 31 is day number one, December 30 is day number two, December 29 is day three, etc., Franklin’s 312 birthday corresponds to day number 349 where the reverse of 349, namely 943, equals 23 times 41 where these two prime numbers differ by 18 (1 plus 17). Further, 23 and 41 are the 9th and 13th prime numbers and interestingly, 9 times 13 gives Franklin’s birth date, 117 (1/17).

Happy 312th birthday, Ben Franklin!

[1] Benjamin Franklin, Wikipedia

https://en.wikipedia.org/wiki/Benjamin_Franklin

[2] A. S. Inan (M. Mangold), Franklin’s 310th: Numerology, *friendsoffranklin.org*, The Friends of Franklin, January 25, 2016.

http://friendsoffranklin.org/?p=447

[3] A. S. Inan, Ben Franklin Turns 310, The Beacon, University of Portland, Portland, Oregon, January 18, 2016.

http://www.upbeacon.com/article/2016/01/ben-franklin-turns-310/

[4] A. S. Inan, “More 17’s in Ben Franklin’s Life,” *Franklin Gazette*, Vol. 21, No. 2, pp. 7-8, Summer, 2011.

[5] A. S. Inan, “Happy 306th Birthday, Ben Franklin!” *Franklin Gazette*, Vol. 21, No. 4, p. 1 and p. 10, Winter, 2011/2012.

[6] A. S. Inan, “The Franklin Number and Other Numerical Oddities in Ben Franklin’s Life,” Vol. 21, No. 3, p. 9, Fall, 2011.

*Aziz Inan is a professor of Electrical Engineering at the University of Portland. He can be reached at **ainan@up.edu**. *