#math trivia for #September14: #257 is a prime of the form 2^(2^n)+1. What is n? Which other day-numbers (1-365) have this form?— Burt Kaliski Jr. (@modulomathy) September 15, 2013 Answer: n = 3 gives 2^(2^n) + 1 = 2^(2^3) + 1 = 2^8 + 1 = 257. Other day-numbers of this form are 3 … Continue reading

# Posted in September 2013 …

## #math trivia #256 solution

#math trivia for #September13: #256 is the last 8th power <= 365. How many years of day-numbers does it take to get to the next 8th power? — Burt Kaliski Jr. (@modulomathy) September 14, 2013 The next 8th power is 38 = 6561. It takes almost 18 years of day-numbers (365 or 366 numbers per … Continue reading

## #math trivia #255 solution

#math trivia for #September12: #255 is the largest 8-bit number. For what n does the largest n-bit number divide 255? Vice versa? — Burt Kaliski Jr. (@modulomathy) September 13, 2013 Only n-bit numbers for n ≤ 8 can possibly divide 255, so let’s consider the largest n-bit numbers for n from 1 to 8. They … Continue reading

## #math trivia #254 solution

#math trivia for #September11: #254 is the product of a prime and a Mersenne prime. What are the primes? — Burt Kaliski Jr. (@modulomathy) September 11, 2013 A Mersenne prime is a prime p that has the form p = 2q-1 where q is also prime. The prime factors of 254 are 2 and 127. … Continue reading

## #math trivia #180 solution

#math trivia for #June28: #180 has prime factorization 2*2*3*3*5 and profile 2+2+3+3+5=15. Is there a larger number with a smaller profile? — Burt Kaliski Jr. (@modulomathy) June 29, 2012 The “profile” of a number is a term I made up for this problem (though others may have used it first). It seemed like a good … Continue reading

## #math trivia #253 solution

#math trivia for #September10: #253 is the product of a Sophie Germain prime and its matching safe prime. What are the primes? — Burt Kaliski Jr. (@modulomathy) September 11, 2013 A Sophie Germain prime is a prime p with the property that 2p+1 is also prime. The prime q = 2p+1 is called the matching … Continue reading

## #math trivia #252 solution

#math trivia for #September9: #252 is divisible by two perfect numbers. What other day-numbers (1-365) have this property? — Burt Kaliski Jr. (@modulomathy) September 9, 2013 There are two perfect numbers that are small enough to divide a day-number, 6 and 28, and they both divide 252. Because the least common multiple of 6 and … Continue reading

## #math trivia #251 solution

#math trivia for #September8: #251 is the largest 8-bit prime. What are the largest 2-, 3-, 4-, 5-, 6- and 7-bit primes? (Why no 1-bits?) — Burt Kaliski Jr. (@modulomathy) September 8, 2013 The largest primes of length 2 to 7 bits are 3, 7, 13, 31, 61, and 127. As it turns out, the … Continue reading

## #math trivia #179 solution

#math trivia for #June27: #179 can be constructed from the digits 1, 7 and 9 using four +s and two *s. How? — Burt Kaliski Jr. (@modulomathy) June 27, 2012 For simplicity, let’s start with the assumption that “from the digits” means that the only numbers input to the equation are the single digits 1, … Continue reading

## #math trivia #250 solution

#math trivia for #September7: #250 cents can be “changed” into dollars and quarters how many ways? How about dollars, quarters and dimes? — Burt Kaliski Jr. (@modulomathy) September 7, 2013 There are three ways to change 250 cents or $2.50 into dollars and quarters, depending on the number of dollars given: Two dollars, two quarters … Continue reading