# 101

This number is a prime. The smallest smoothly undulating palindromic prime (SUPP). Australia's sugar industry once imported 101 cane toads from Hawaii in the hope that they would kill cane beetles threatening their sugar crop. 101 = 5! - 4! + 3! - 2! + 1! Depeche Mode named one of their albums "101". [Gevisier] The 101 proof of the Kentucky bourbon Wild Turkey is its most common bottling. 101 = 13 + 17 + 19 + 23 + 29 (the sum of five consecutive primes). [De Geest] Using the alphabet code A = 1, B = 2, C = 3, ... , Z = 26: D + I + V + I + S + I + O + N = 101. [Cox] The plot of Walt Disney's cartoon film One Hundred and One Dalmatians (often abbreviated as 101 Dalmatians) centers on the fate of the kidnapped puppies of Pongo and Perdita. 101 is the largest known prime of the form 10n + 1. [Kulsha] Author James Branch Cabell was born at 101 East Franklin Street, Richmond, Virginia. 101 is the smallest odd prime such that p - k! for 1 ≤ k! < p is composite. [Russo] The only known prime of the form 10k1. [Goldstein] Room 101 was the place where your worst fears were realized in George Orwell's classic Nineteen Eighty-Four. Professor Nash's office number in the movie A Beautiful Mind. The Challenge Coin was issued to Vietnam Veterans of the 101st Airborne Division. [Ziccardi] The number of digits in the product of the 39 successive primes produced by the formula n2 + n + 41, where n = 1 to 39. This formula was used by Charles Babbage to demonstrate the capabilities of his Difference Engine (1819-1822). [Haga] Combine two digits of a number in order (from right to left) alternating them with + then -. If the result is 0 or a multiple of 101, the prime number 101 divides it. E.g., Is 575519513 divisible by 101? 13 - 95 + 51 - 75 + 05 = -101. Yes! [Luhn] The largest prime factor of smallest palindromic Carmichael number (101101). [Gupta] The only 3-digit prime such that the sum of each of its digits raised to itself is prime, i.e., 1^101+0^101+1^101 = 2 is prime. [Loungrides] Queen Elizabeth the Queen Mother was 101 when she died on Easter Saturday 2002. [Croll] The smallest palindromic prime p such that largest odd factor of p-1 is a non-prime (i.e., composite or 1). [Russo] Thor Heyerdahl's book Kon-Tiki is about his harrowing 101-day feat of crossing the Pacific on a balsa log raft which made him world famous. The smallest odd prime which can be represented as the sum of a square and its reverse, i.e., 100 + 001 = 101. [Gupta] The concatenation of all palindromes from 1 up to 101 is prime. [De Geest] The greatest prime factor of any 4-digit repdigit is 101. [La Haye] The Math Forum was one of PC Magazine's Top 101 Most Incredibly Useful Web sites in the Information category for the year 2003. Room 101 is the name of a British TV series in which celebrities are invited to discuss their (often whimsical) pet hates with the host. In a short section titled "Prime Numbers ... and Monkeys" of Danica McKellar's bestselling book Math Doesn't Suck, the following statement can be found: "It's hard to believe that there's no way to evenly divide up 101, but it's true!" Christopher Hornsrud, Prime Minister of Norway in 1928, is believed to be the longest lived Prime Minister of any country. He died at age 101. [Duffy] The number 101^2 + 97^2 +...+ 3^2 + 2^2 is prime. [Patterson] A radio astronomer in the movie Contact makes the statement "OK, a hundred and one, the pulse sequence through every prime number between two and a hundred and one." [Haas] Aging 101 is a series of general information articles on aging that school teachers and their students can use in a variety of courses. Its intent is to have you make it until at least 101 years of age. 101^101-100^100+99^99-98^98+...-2^2+1^1 is prime. Note that 101 is the only known odd prime p, such that p^p-(p-1)^(p-1)+...-2^2+1^1 is prime. [Firoozbakht] The British lost interest in airships because of the crash of R-101. Taipei 101 (pronounced "one oh one" in English) comprises 101 floors above ground. It is located in Xinyi District, Taipei, Taiwan. [Post] The last five digits of 101^101 are 10101. [Hu] 101 is the sum of all products p*q involving the four first primes, i.e., 2*3 + 2*5 + 2*7 + 3*5 + 3*7 + 5*7. [Gallardo] 101 is a common solution of the following four equations: 8^N+N=prime, 3^N-2^N=prime, 12^N-11^N=prime, and 75^N-74^N=prime. [Simon] The first odd prime for which the Mertens function M(n) = 0. [Post] 101 is the 26th prime number. The 26th element on the periodic table is iron (Fe). The word "iron" appears 101 times in the Bible (KJV). [Slattery] 101 is the first three-digit prime number that can be both read backward and upside-down without being changed. [Mosse] A googol (10^100) contains 101 digits. The search engine Google's play on the term reflects the company's mission to organize the immense amount of information available on the web. "The 101 Car" is used as the Regional Tourist Information Center in Big Stone Gap, Virginia. The smallest prime which requires a multidigit prime number of digits (base 10) and a prime number of chisel strokes as a sans serif Roman numeral. Curiously, this is true whether one considers "C" to be one stroke (a circular arc) or two strokes (like a left angle-bracket or less-than sign). [Post] The smallest prime with digit 0. [Beedassy] "Hundred and one" represents one of the 101 partitions of the letters used in this order. [Beedassy] -101 + 9789837973716761595347434137312923191713117532 is prime. Note the descending concatenation of all primes smaller than 101. [Silva] The sum of the first eight semiprimes. [Silva] The smallest palindromic prime that uses a prime number of distinct nonprime digits. [Beedassy] The smallest Cyclops prime. [Pol] The smallest anti-Yarborough prime (i.e., made up of digits 0 and 1 only) whose binary representation (11001012) is also an anti-Yarborough prime in base ten. [Beedassy] The sum of the first 11 non-composite numbers. Note that 11 and 101 are the first two palindromic primes. [Silva] It is not unlikely to hear prime numbers discussed on the 101st day of the year. The smallest palindromic irregular prime. [Poo Sung] The smallest prime number that is displayed on a 12-hour digital clock. [Fellows] The first prime that in figures and words (in UK spelling) includes both the first numerical digit (101) and the first alphabetical letter (one hundred and one). [Beedassy] The 5th centered decagonal number (numbers of the form 5(n^2 - n) + 1). [Green] Smallest prime whose every power contain the digit zero in it. [Gupta] Something 101 (pronounced 'one-oh-one') in popular slang is the beginning or introductory lessons required for any understanding, as in 'Home Buying 101' or 'Prime Numbers 101'. [Green] 101 (base b) is a near-square number in every base b and it is conjectured that there are infinitely many bases for which 101 is prime. [Green] The smallest canyon prime. [Pol] The only known prime p such that sigma(p-1) = sigma(p+1) + 1. [Firoozbakht]

POWERS OF 101 - PASCALINDROMES
The first five consecutive powers of 101 produce
palindromes. The next 4 consecutive powers of 101
produce 'quasi-palindromes' in the sense of
concatenating several multidigit numbers in reverse
order, but not reversing the digits of those individual
numbers. In all these powers the numbers in the rows
of Pascal's Triangle can be seen in order (with some
zeros thrown in here and there so that each number,
after the first, occupies a two-digit space), hence the
name 'Pa-sca-lindromes'.
1010 = 1
1011 = 101
1012 = 10201
1013 = 1030301
1014 = 104060401
1015 = 10510100501
1016 = 1061520150601
1017 = 107213535210701
1018 = 10828567056280801
[Green] The number of Christmas Trees in Mary Ellen Yanich's Library. In the classic fairy tale Sleeping Beauty, the lovely princess was awakened back to life by a smitten prince's kiss laid on the 101th year following her accidentally prick-induced trance, in accordance with the attenuated curse. [Beedassy] The palindromic ZIP Code of Brimfield MA is 101 with a zero on each end. The only 3-digit number whose digits are neither prime nor composite. [Gudipati] ROCKY MOUNTAIN * PRIME * in Aurora, Colorado, features "STEAKS & COOKING 101" on their website. The largest prime with the smallest sum of digits. [Loungrides] Primitive artist Grandma Moses died at the age of 101. The Mathematical Association of America offers a book about careers in mathematics titled 101 Careers in Mathematics. So Who Hires Math Majors anyway? The first of 21 consecutive primes that remain primes if you eliminate their central digit. [Loungrides] If A = 2 (base 2) = 10, B = 3 (base 3) = 11, C = 5 (base 5) = 12, ..., then "PRIMECURIOS" is 101. [Beedassy] The (1!*0!*1!)st (1!+0!+1!)-digit prime is 101. [Worrom] 101 is the sum of the first 1001 (base two) primes plus 1. [Kawashima] www.101science.com is a website serving Science and Technology. The only binary Cyclops prime. [Pampena] The smallest prime whose cube does not divide at least one ten-digit pandigital number. [Gaydos] The 101st Fibonacci number ends with 101. To explore how prime and composite numbers affect us in our everyday lives, students at Northridge Elementary in Longmont, Colorado, took on an interesting design challenge. They were given a scenario in which they had 101 guests to distribute evenly. Shop 101 is India's leading social commerce platform which enables entrepreneurs to sell online as well as with WhatsApp, Facebook and Instagram. [Homewood] Prime Numbers 101: Consider the first four primes, i.e., 2, 3, 5, 7. Now, 2*3 + 5*7 = 41, 2*5 + 3*7 = 31, and 2*7 + 3*5 = 29 (all prime). Let's add them: 41 + 31 + 29 = 101. [Bui Quang Tuan] There are exactly 101 numbers n such that n and the nth prime together use only distinct digits. [Seidov] The 101st and 102nd centuries are the smallest pair of consecutive centuries to have no years that are powers of other numbers, i.e., no squares, cubes, 4th powers, etc. [Gaydos] The first to land both pawns on 101 wins in the mathematical board game "Prime Climb." The smallest palindromic prime that is the sum of three distinct primes with distinct prime digits, i.e., 101 = 5 + 23 + 73. [Sariyar] The "Chesterfield 101" cigarette was advertised as being just a silly millimeter longer. [Gaydos]

(There are 61 curios for this number that have not yet been approved by an editor.)