# 103

This number is a prime. The smallest prime whose reciprocal contains a period that is exactly 1/3 of the maximum length. [Wells] Illinois has two area codes that are multiples of 103: 309 (3 * 103) and 618 (6 * 103). [Litman] Proof, an award-winning play by David Auburn, revolves around a mysterious mathematical proof involving prime numbers left behind in 103 notebooks by a young woman's brilliant father. The least integer which is not sum or difference of two integers all whose prime factors are 2 and 3. [Crespi de Valldaura] The world's largest tree is the General Sherman Tree, a sequoia in Sequoia National Park, California. Its trunk is roughly 103 feet in circumference. [Jolly] The smallest prime comparable to all minimal primes in base 4. [Rupinski] 3 and 103 are prime, as are 3*2^103-1 and 103*2^3-1. There is no other pair of primes less than 1000 with this property. [Hartley] 103 + (10!)^3 is prime. [Patterson] M103 and NGC 103 are both open clusters of stars in Cassiopeia. [Necula] 103 divides the concatenation of the integers 103 down to 1. [De Geest] There are exactly 103 geometrical forms of magic knight's tour of the chessboard. Using a standard dartboard, 103 is the lowest possible prime that cannot be scored with two darts. Astronomer Charles Messier cataloged 103 objects in his list of nebulae. [McCranie] The smallest Cyclops prime that's also a twin, a cousin, and a sexy prime. [Punches] One Hundred and Three is a poem by Henry Lawson (often called Australia's "greatest writer") about his prison number. The smallest positive integer with no double-base representation of length 2. (Vassil S. Dimitrov, Everett W. Howe, Lower bounds on the lengths of double-base representations, January 23, 2010). [Post] Operation Entebbe involved the Israeli rescue of 103 hostages from a French airliner hijacked by members of the Palestine Liberation Organization. 103 is the sum of the second digits of all two-digit primes. [Silva] The smallest prime p such that reversal(p*reversal(p)) is prime. [Loungrides] The largest distinct-digit reflectable prime. Note that there are only five such primes, i.e., 3, 13, 31, 83, 103. [Loungrides] In the movie, "Naked Gun 2 1/2," the number of the bus under which "Nordberg" becomes stuck is 103. "Prime Cutz" Barbershop is located at 103 Courthouse Square in Jonesborough, TN. The prime with a partition into prime parts using the most distinct digits: 103 = 2 + 5 + 7 + 89. [Beedassy] The book 103 Mathematical Curiosities: Theory of Numbers, Figures and Relationships in Contemporary Mathematics by Pietro Paolo Lava and Giorgio Balzarotti deals with 103 short monographic chapters on various topics of mathematics concerning the theory of numbers. The only Lucas-Wieferich prime less than a billion. [Luen] (103, 107) is the first cousin prime pair (p, q) such that p^2+q^3 -/+ 1 is a twin prime pair, i.e, (1235651, 1235653). [Loungrides] The product of all primes with distinct prime digits minus 103 is prime. [Loungrides] The "Gödel Code" for the word FOXTROT contains 103 decimal digits. Longer than any letter in the NATO Phonetic Alphabet (Alfa-Zulu). [Honaker]

```A 116252718750​,
B 126549297400319587938067556680330478718512220​,
C 20194901948267217839018728287420415124151392820360​,
D 833143468021550307316406250000​,
E 1602302009605762500000,
F 5051690607024954179010179893239071469494516923352311358251857714821860897146935224605560302734375000000​,
G 52754204988843750000000,
H 18478269411645510070000708007812500000000,
I 67939538643524160000,
J 1312736671231405826729030115169078090910076550483224710581928719180917750000000000,
K 46723126600104034500000000000,
L 688905000000000000​,
M 132324872400000000000,
N 8125874138560062910137743601493047743667635427563822773710937500000000000000,
O 185280690471924772779927545401344000,
P 210000000000000000,
Q 74284098949096853302886400000,
R 322366034239817959383642175680000000000000,
S 3795662919494318722708025280474805080475238400000,
T 66050754992353410652665600000000000000,
U 10723890009193816615419130183121829604565018053348609927956523266048000000000,
V 386805489821561152262500957843301996383380003645661756342665216000,
W 749052176126504624234060514486543964496375917554490041332742511040151552000000000,
X 43583638688782314429699855241539747840,
Y 72645686886652946011545600000000000000,
Z 95724945709235937630308342513664000000000000.
``` The only prime that can be represented in four ways as sum of a double-digit prime plus the reversal of another double-digit prime, i.e., 11+R(29), 29+R(47), 71+R(23), 89+R(41). [Loungrides] The number of digits in the first counterexample (2341) to the converse of Fermat's Little Theorem that is said to have eluded the computational skills of ancient Chinese, circa 500 BC. [Beedassy] 103 is the smallest prime not found in the first thousand digits of π. These digits of π count the initial digit "3" and 999 decimal digits. Note that the same applies to the prime 107 while the prime 109 already appears in the first thousand digits of π. [Rivera] There are 103 species of beetle native to the Indonesian island of Sulawesi. [Homewood] If A = 1, B = 4, C = 1, ... , Z = 8, using the decimal digits of π, then 'TWIN PRIME CONJECTURE' is a twin prime. [Homewood] The smallest prime which cannot be expressed as a sum or difference of two numbers which contain only the factors 2 and 3. That is, 103 cannot be written in either of these forms: 2^x + 3^y = 103, 2^x - 3^y = 103, 3^y - 2^x = 103, 2^x3^y +/- 1 = 103. [Diloreto] The smallest multidigit prime that can be represented as an illustration of Wilson's theorem as the only 3-digit such prime, i.e., (6!+1)/7=103. [Loungrides] 103 is a prime with a digit 3 and equals the ascending sum of 3 primes each with a digit 3 where the 3 "non-digit 3" digits {2,7,4} sum to 13 (also prime with a digit 3). Note that π(103) = 3*3*3. [Worrom] The emergency telephone number for an ambulance in Ukraine. [Engels] Prime Numbers Technology (PNT) is located at Suite 103 in Marborough, Massachusetts. Andrew Jackson fought 103 duels—most of them to defend his wife's honor. [Bonney]

(There are 2 curios for this number that have not yet been approved by an editor.)