17 Number Facts about 2017 in 2:17

2:17

2016-12-31

[public] 181K views, 6.34K likes, 122 dislikes audio only

Stand-up Maths

Here are all the facts and references!

FACT 01: It’s a prime number

Last: 2011, Next: 2027

https://primes.utm.edu/lists/small/1000.txt

FACT 02: Has a digit sum 10

Last: 2008, Next: 2026

Add them up yourself!

FACT 03: Has 11 distinct letters

Last: 2009, Next: 2019

Here they are: adehnostuvw

FACT 04: No letters in common with “Prickly fig”

Last: 2010, Next: 7000

Look, none of these: cfgiklpry

FACT 05: It is the sum of two squares

Last: 2009, Next: 2018

9^2 + 44^2

https://oeis.org/A001481

FACT 06: Prime one more than multiple of 4

Last: 1997, Next: 2029

These are called Pythagorean Primes.

http://oeis.org/A002144

FACT 07: Prime one more than multiple of 8

Last: 1993, Next: 2081

http://oeis.org/A007519

FACT 08: Prime one more than a multiple of 16

Last: 1889, Next: 2081

http://oeis.org/A094407

FACT 09: Prime one more than a multiple of 32

Last: 1889, Next: 2081

http://oeis.org/A133870

FACT 10: “2017” is a prime in base 8

Last: 2011, Next: 2111

In base 8, 2017 is 1039.

http://oeis.org/A235394

FACT 11: Prime of the form a^2 + b^4

Last: 1777, Next: 2069

http://oeis.org/A028916

FACT 12: I turn a prime age in a prime year

Last: 2011, Next: 2027

It’s just one of those things I keep track of.

FACT 13: Number n such that both n and (n+1)/2 are primes

Last: 1993, Next: 2137

http://oeis.org/A005383

FACT 14 Lower prime of a difference of 10 between consecutive primes

Last: 1879, Next: 2029

http://oeis.org/A031928

Here is a list of the largest gaps:

https://primes.utm.edu/notes/GapsTable.html

FACT 15: Smallest palindrome greater than n in bases n and n+1

Last: 1892, Next: 2146

Other numbers are smaller in other pairs of bases. 2017 is the smallest for bases 31 and 32.

232 in base 31, 1v1 in base 32 (v=31)

http://oeis.org/A048268

FACT 16: It's not 2016

Last: 2015, Next: 2018

A calendar.

FACT 17: Number of permutations of n elements not containing the consecutive pattern 123

Last: 349, Next: 13,358

http://oeis.org/A049774

CORRECTIONS:

- At 1:50 I accidentally say "prime" when I mean "palindrome". First spotted by Oliver Feghali.

- I accidentally gave the prime gap after 1327 as the number of non-prime years in-between (33) and not the increase to the next prime (34) like I did for all the others. Sorry, that was me combining two bits of research without thinking! I should have spotted the jarring mismatch of odd and even intervals and realised I was not bring consistent. Pointed out by loads of people, the first of which was TheActualNuttmegger.

- The 22 year prime gap ended in the 1970s, not started then (1951 to 1973). Spotted by Scottish Chemist.

- For fact 17, it is actually the permutations for n=7, not 8; caught by trigonzobob. The permutation conditions are also more complicated that I managed to explain as well ("without double falls"). Check out http://oeis.org/A049774

- Let me know if you spot anything else.

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MATT PARKER: Stand-up Mathematician