## 1999

© Copyright 1999, Jim Loy

Let me ask a few questions about 1999:

1. What is 1999 in binary (base 2)?
2. Is 1999 prime or composite?
3. If it is composite, what are its factors?
4. What is the next year after 1999 that is prime?
5. Is 1999 part of a twin prime pair (two consecutive odd numbers that are both primes)?
6. What is the next year after 1999 that is part of a twin prime pair?
7. Is 1999 a square?
8. What is the next year that is a square?
9. What is the previous year that was a square?
10. Is 1999 the sum of three primes?
11. What is the next year that is the sum of three primes?
12. Is 1999 a cube?
13. What is the next year that is a cube?
14. What is the previous year that was a cube?
15. What is the next year that is a factorial?
16. What is the next year that is a power of 2?
17. What is the next year that is a 4th power of some integer?
18. What is the next year that is a 5th power of some integer?
19. What is the next year that is a 6th power of some integer?
20. What is the next year that is a 7th power of some integer?
21. What is the next year that is a 8th power of some integer?
22. What is the next year that is a 9th power of some integer?
23. What is the next year that is a 10th power of some integer?
24. What is the next year that is a 11th power of some integer?
25. What is the next year that is a Fibonacci Number (1, 1, 2, 3, 5, 8, 13, 21..., each number being the sum of the previous two numbers)?
26. What is the next year that is a Perfect Number (an integer that is the sum of its proper divisors (including 1 but not including itself), example: 28=1+2+4+7+14?
27. What year is the next palindromic number (same forward and backward)?
28. What year is the next triangular number (number of dots arranged in a triangular array like bowling pins)?
29. When is the next year that is a semiprime (has exactly two prime factors)?
30. Is 1999 the sum of two consecutive integers?
31. What is 1999/9999?

Answers:

1. What is 1999 in binary (base 2)? 11111001111 (1024 + 512 + 256 + 128 + 64 + 8 + 4 + 2 + 1).
2. Is 1999 prime or composite? Prime. Just try dividing by every prime < 44.
3. If it is composite, what are its factors? Sorry, it is prime.
4. What is the next year after 1999 that is prime? 2003
5. Is 1999 part of a twin prime pair (two consecutive odd numbers that are both primes)? Yes, 1997 & 1999 are primes.
6. What is the next year after 1999 that is part of a twin prime pair? 2027.
7. Is 1999 a square? Of course not, it is a prime.
8. What is the next year that is a square? 2025 (45 squared).
9. What is the previous year that was a square? 1936 (44 squared).
10. Is 1999 the sum of three primes? Yes, one version of Goldbach's Conjecture is that every integer greater than 5 is the sum of three primes, and has been checked for numbers into the many billions.
11. What is the next year that is the sum of three primes? 2000. A more famous version of Goldbach's Conjecture is that every even integer > 3 is the sum of two primes. So 1998 is the sum of two primes, and 2000 (1998+2) is the sum of three primes.
12. Is 1999 a cube? No, it is prime.
13. What is the next year that is a cube? 2197 (13 cubed)
14. What is the previous year that was a cube? 1728 (12 cubed).
15. What is the next year that is a factorial? 5040 (7!).
16. What is the next year that is a power of 2? 2048 (2 to the 11th).
17. What is the next year that is a 4th power of some integer? 2401 (7 to the 4th).
18. What is the next year that is a 5th power of some integer? 3125 (5 to the 5th).
19. What is the next year that is a 6th power of some integer? 4096 (4 to the 6th).
20. What is the next year that is a 7th power of some integer? 2187 (3 to the 7th).
21. What is the next year that is a 8th power of some integer? 6561 (3 to the 8th).
22. What is the next year that is a 9th power of some integer? 19683 (3 to the 9th).
23. What is the next year that is a 10th power of some integer? 59049 (3 to the 10th)
24. What is the next year that is a 11th power of some integer? 2048 (see #16 above)
25. What is the next year that is a Fibonacci Number (1, 1, 2, 3, 5, 8, 13, 21..., each number being the sum of the previous two numbers)? 2584. You may just have to calculate the first 28 numbers in the series.
26. What is the next year that is a Perfect Number (an integer that is the sum of its proper divisors (including 1 but not including itself)? 8128, the fourth perfect number. The formula for even perfect numbers is that if 2p-1 [that is (2^p)-1] is prime, then 2p-1(2p-1) [that is 2^(p-1)((2^p)-1)] is a perfect number. There are no known odd perfect numbers.
27. What year is the next palindromic number (same forward and backward)? 2002.
28. What year is the next triangular number (number of dots arranged in a triangular array like bowling pins)? 2016. The formula is n(n+1)/2, which is also the sum of the first n integers.
29. When is the next year that is a semiprime (has exactly two prime factors)? 2005 is 5x401.
30. Is 1999 the sum of two consecutive integers? Yes, every odd integer is.
31. What is 1999/9999? 0.1999199919991999... (1999 repeated forever). This works for any year of 4 digits.