Category Archives: Numbers

Converting Between Julian Dates and Gregorian Calendar Dates in Fortran (and JavaScript)

When looking through some of my old papers I found at my father’s house after he died, I found some old Fortran code for converting Gergorian calendar dates to and from Julian dates. I haven’t used Fortran since the 1970s, so the code looked a little strange.

Some examples of Julian dates:

Julian Date Equivalent Gregorian Date
2369916.0 July 4, 1776 12:00:00.0 UT
2436911.509722 December 9, 1959 00:14:00.0 UT (the time of my birth)
2457533.5 May 25, 2016 00:00:00.0 UT

Julian dates are a continuous count of days since Greenwich Mean Noon on January 1, 4713 BCE. January 1, 4713 BCE is also known as -4712 January 1 when used for astronomical calculations. The apparent one year difference is due to there being no year 0—the day after December 31, 1 BCE was January 1, 1 CE. It makes adding and subtracting dates easier.

Greenwich Mean Noon is 12:00 noon UT (Universal Time). UT is a time standard based on Earth’s rotation. It is a modern continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the Prime Meridian at Greenwich, London, UK. In fact, the expression “Universal Time” is ambiguous when accuracy of better than a few seconds is required, as there are several versions of it, the most commonly used being Coordinated Universal Time (UTC) and UT1. All of these versions of UT, except for UTC, are based on Earth’s rotation relative to distant celestial objects (stars and quasars), but with a scaling factor and other adjustments to make them closer to solar time. UTC, on the other hand, is based on International Atomic Time, with leap seconds added to keep it within 0.9 second of UT1.

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Truncating Numbers in JavaScript

I needed a function to truncate a number. Math.floor() worked … until I tried it on a negative number.

So I had to write my own truncate function. Even though I needed to truncate numbers to the integer portion only, I figured sooner or later I would need to truncate to a given number of decimal places. This function does that.

<script>// <![CDATA[
function ccTruncate(number, places) {
    var shift = Math.pow(10, places);
    return ((number * shift) | 0) / shift;
};
// ]]></script>

If you find this useful, let me know in the comments below.

Telephone Exchange Names

This article is still being worked on, but I wanted to share it before it was completed. If you want to be notified when it is updated leave a comment below.

When I was a child I lived in San Bernardino, California from 1966 to 1969. I can still remember my home telephone number: TUrner 5-2176, sometimes abbreviated as TU 5-2176. My grandparents’ telephone number was TU 3-5155.

If I wanted to call my grandparents, since we both lived in the TUrner area, I only had to dial 3-5155. But if I called someone outside the TUrner area, I had to include the two letters, for example, to call someone at UNion 4-7721 I had to dial 864-7721.

So what or who was TUrner?

The Central Office

Prior to 1955, many people had been using exchange names that were not included in the official list and they were not required to change them. For example, I remember advertisements on television urging me to call RIchmond 9-5171 to go see Championship Wrestling at the Olympic Auditorium in Los Angeles. The official exchange names were PIlgrim, PIoneer, RIverside, RIverview, SHadyside, and SHerwood.

The National Numbering Plan

The National Number consists of ten digits as follows.

Table 1. Composition of the National Number.
Listed Directory Number
Area Code Office Code Station Number
X1 X2 X3 L L N N N N N

Where
L = Any letter from Table 2 below.
N = Any numeral from 0 to 9.
X1 = Any numeral from 2 to 9.
X2 = 0 (zero) or 1.
X3 = Any numeral from 0 to 9 when X2 = 0. Any numeral from 0 to 9 except 1 when X2 = 1.

Table 2. Dial Pulses Corresponding to the Letters of the Office Code Portion of the National Number.
Letters No. of Dial Pulses
A   B   C 2
D   E   F 3
G   H   I 4
J   K   L 5
M   N   O 6
P   R   S 7
T   U   V 8
W   X   Y 9

The information in Tables 1 and 2 was taken from “Section II Chart 1: The National Numbering Plan” in Notes on Nationwide Dialing (1955).

List of Suitable Central Office Names

Table 3. List of Suitable Central Office Names.
22 23 24 25 26 27 28 29
ACademy
BAldwin
CAnal
CApital
CAstle
ADams
BElmont
BEverly
CEdar
CEnter
CEntral
CHapel
CHerry
CHestnut
CHurchill
CIrcle
ALpine
BLackburn
CLearbrook
CLearwater
CLifford
CLinton
AMherst
ANdrew
ANdrews
COlfax
COlony
COngress
BRidge
BRoad
BRoadway
BRown
BRowning
CRestview
CRestwood
ATlantic
ATlas
ATwater
AVenue
BUtler
AXminster
AXtel
CYpress
32 33 34 35 36 37 38 39
DAvenport
DAvis
EAst
EAstgate
FAculty
FAirfax
FAirview
DEerfield
DEwey
EDgewater
EDgewood
EDison
FEderal
DIamond
DIckens
FIeldbrook
FIeldstone
FIllmore
FIreside
ELgin
ELliot
ELmwood
FLanders
FLeetwood
EMerson
EMpire
ENdicott
FOrest
FOxcroft
DRake
DRexel
ESsex
FRanklin
FRontier
DUdley
DUnkirk
DUpont
EVergreen
FUlton
EXbrook
EXeter
EXport
EXpress
42 43 44 45 46 47 48 49
GArden
GArfield
HAmilton
HArrison
HAzel
GEneral
GEneva
HEmlock
HEmpstead
IDlewood
GIbson
GIlbert
HIckman
HIckory
HIllcrest
HIlltop
GLadstone
GLencourt
GLendale
GLenview
GLobe
HObart
HOmestead
HOpkins
HOward
INgersoll
GRanite
GReenwood
GReenfield
GReenleaf
GRover
GRidley
HUbbard
HUdson
HUnter
HUntley
HUxley
IVanhoe
GYpsy
HYacinth
HYatt
52 53 54 55 56 57 58 59
JAckson
LAfayette
LAkeside
LAkeview
LAmbert
LAwrence
JEfferson
KEllogg
KEystone
LEhigh
LEnox
KImball
KIngsdale
KIngswood
LIberty
LIncoln
LInden
Reserved
for radio
telephone
JOhn
JOrdan
LOcust
LOgan
LOwell
Reserved
for radio
telephone
JUniper
JUno
JUstice
LUdlow
LUther
LYceum
LYndhurst
LYnwood
LYric
62 63 64 65 66 67 68 69
MAdison
MAin
MArket
MAyfair
NAtional
MEdford
MElrose
MErcury
NEptune
NEwton
NEwtown
MIdway
MIlton
MIssion
MItchell
NIagara
OLdfield
OLive
OLiver
OLympia
OLympic
MOhawk
MOntrose
MOrris
NOrmandy
NOrth
NOrthfield
ORange
ORchard
ORiole
ORleans
OSborne
MUrdock
MUrray
MUseum
MUtual
OVerbrook
OVerland
MYrtle
OWen
OXbow
OXford
72 73 74 75 76 77 78 79
PAlace
PArk
PArkview
PArkway
RAndolph
RAymond
SAratoga
PErshing
REdfield
REdwood
REgent
REpublic
PIlgrim
PIoneer
RIverside
RIverview
SHadyside
SHerwood
PLateau
PLaza
PLeasant
PLymouth
SKyline
POplar
POrter
ROckwell
ROger
ROgers
SOuth
SOuthfield
PRescott
PResident
PRospect
SPring
SPruce
STate
STerling
STillwell
STory
SUnset
PYramid
SWathmore
SWift
SWinburne
SYcamore
82 83 84 85 86 87 88 89
TAlbot
TAlmadge
TAylor
VAlley
VAndyke
TEmple
TEnnyson
TErminal
TErrace
VErnon
THornwall
TIlden
VIctor
VIctoria
VIking
VInewood
ULrick
ULster
ULysses
TOwnsend
UNderhill
UNion
UNiversity
VOlunteer
TRemont
TRiangle
TRinity
TRojan
UPtown
TUcker
TUlip
TUrner
TUxedo
TWilight
TWinbrook
TWinoaks
TWining
92 93 94 95 96 97 98 99
WAbash
WAlker
WAlnut
WArwick
WAverly
WEbster
WElls
WEllington
WEst
WEstmore
YEllowstone
WHitehall
WHitney
WIlliam
WIlliams
WIlson
WIndsor
Reserved
for radio
telephone
WOodland
WOodlawn
WOodward
WOrth
YOrktown
Reserved
for radio
telephone
YUkon WYandotte
WYndown
WYman

The information in Table 3 was taken from “Section II Appendix A: List of Suitable Central Office Names” in Notes on Nationwide Dialing (1955).

References

American Telephone and Telegraph Company. Notes on Nationwide Dialing. 1955.

Palindromic Prime Numbers, Part 2

So the question was asked on this page, “Are there any four-digit prime numbers?”

Stop here and go to the other page if you want to read the first part about palindromic prime numbers and try to answer the question before reading the answer below.


You’re still here, so here’s the answer.

No. There are no four-digit palindromic prime numbers. There are also no six-digit, eight-digit, or other even-number-of-digits palindromic prime numbers, except the two-digit 11.

Every even-number-of-digits palindromic number is evenly divisible by 11.

There is an easy test to see if a number is evenly divisible by 11. Take the digits of the number and, starting with the left side going toward the right side, alternate between subtracting and adding the digits. If the total is 0 or a multiple of 11, the number is evenly divisible by 11, otherwise it is not evenly divisible by 11. Here are some examples with five-digit palindromic prime numbers:

10,301 (the smallest five-digit palindromic prime) is not evenly divisible by 11 because:

1 – 0 + 3 – 0 + 1 = 5     (10,301 ÷ 11 = 936.45…).

14,641 is evenly divisible by 11 because:

1 – 4 + 6 – 4 + 1 = 0     (14,641 ÷ 11 = 1,331).

98,689 (the largest five-digit palindromic prime) is not divisible by 11 because:

9 – 8 + 6 – 8 + 9 = 8     (98,689 ÷ 8971.72…)

Four-digit palindromic numbers follow the pattern “abba”, for example, 1221, 6446, and 8228. When calculating whether or not the number is evenly divisible by 11, we end up with:

ab + ba

This pattern will always result in 0 because we are adding an a and subtracting an a, subtracting a b and adding a b. This also applies to all other even-digit palindromic numbers.


Here is a list of all the four-digit prime numbers in case you want to check it out for yourself:

1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, and 9973.

Palindromic Prime Numbers, Part 1

A palindrome /ˈpælɪndroʊm/ is a word, phrase, number, or any other sequence of units which reads the same forwards as it does backwards. Examples of palindromes are the words sees, radar, madam, and aibohphobia (fear of palindromes); the sentences, “Rise to vote sir”, “Too hot to hoot”, “A war at Tarawa!”, and “Noel sees Leon”; and the numbers 44, 212, 6,776, and 12,321.

A prime number is any natural number that is greater than 1 and is divisible only by itself and 1. Examples of prime numbers are 2, 3, 5, 7, 11, and 13.

There are many palindromic prime numbers, for example, 11, 101, 373, and 10,301. Are there any four-digit prime numbers?

Click here for the answer.


Fun facts: 1010000 + 222999222*104996 + 1 is the smallest 10,001-digit palindromic prime number. 1010001 – 6192916*104997 – 1 is the largest 10,001-digit palindromic prime number.

The Number 83

Miscellaneous

83 is the atomic number of bismuth (symbol Bi).

In Judaism, when someone reaches 83 years old they may celebrate a second bar mitzvah. The Torah says that a normal lifespan is 70 years, so an 83-year-old person can be considered 13 years old in a second lifetime.

83 is the highest UHF channel on older televisions made before the late 1970s (newer televisions only go up to channel 69, due to the frequency spectrum previously assigned to channels 70–83 in the USA being reassigned to cellular phone service there in the late 1970s–early 1980s).

The 83rd day of the year in the Gregorian calendar is March 24 in non-leap years, March 23 in leap years.

The Bell XP-83 (later redesignated ZXF-83) was a United States prototype escort fighter designed by Bell Aircraft during World War II. It first flew in 1945. As an early jet fighter, its limitations included a lack of power and it was soon eclipsed by more advanced designs.

The B83 thermonuclear bomb is a variable-yield gravity bomb developed by the United States in the late 1970s, entering service in 1983. With a maximum yield of 1.2 megatonnes of TNT (75 times the yield of the atomic bomb “Little Boy” dropped on Hiroshima on August 6, 1945, which had a yield of 16 kilotonnes of TNT), it is the most powerful nuclear free-fall weapon in the United States arsenal. The first underground test detonation of the production B83 took place on December 15, 1984.

HLA-B*83 (B83) is an HLA-B allele-group composed of a single allele, B*8301. There is no useful serology associated with this allele. It is found in a single Mbenzele Pygmy tribe of the Central Africa Republic.

Interstate 83 (abbreviated I-83) is an Interstate Highway in the Eastern United States that runs from Baltimore, Maryland to Harrisburg, Pennsylvania.

83 is the ISBN Group Identifier for books published in Poland. The International Standard Book Number (ISBN) is a unique numeric commercial book identifier assigned to each edition and variation (except reprintings) of a book. For example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 10 digits long if it was assigned on or before December 31, 2006 and 13 digits long if assigned on or after January 1, 2007.

83 is slang for a bisexual person. It is derived from the atomic number of bismuth which has the symbol Bi.

83 is a glasses-wearing variation of the :3 emoticon. The :3 emoticon represents the cat face made by anime characters when they say something clever or sarcastic, or are commenting on something cute.


Prime Numbers

83 is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

83 is the 23rd prime number. 23 is also a prime number. The previous prime number is 79 and the next prime number is 89.

79 and 83 are cousin primes. Cousin primes are prime numbers that differ by four. Twin primes are pairs of prime numbers that differ by two, and sexy primes are pairs of prime numbers that differ by six. The term “sexy prime” stems from the Latin word for six: sex.

83 is the sum of three consecutive prime numbers: 23 + 29 + 31.

83 is the sum of five consecutive primes: 11 + 13 + 17 + 19 + 23.


Astronomy

Messier object M83, also known as the Southern Pinwheel galaxy, is a magnitude 8.5, barred spiral galaxy, 15 million light-years away in the constellation Hydra. M83 is classified as a barred spiral galaxy due to the bar-like pattern of stars that run through its center, very similar in structure to our own Milky Way galaxy. More info.

New General Catalogue object NGC 83 is a magnitude 14.2, a lenticular galaxy, 285–330 million light-years away in the constellation Andromeda. NGC 83 was discovered by John Herschel on August 17, 1828. More info.

Solar eclipse saros series 83 contained 71 solar eclipses over a period of 1,262.11 years, beginning on May 5, 210 BCE and ended on May 30, 1052. More info.

Lunar eclipse saros series 83 contained 84 lunar eclipses over a period of 1,496.50 years, beginning on August 22, 197 BCE and ended on February 5, 1300. More info.

The saros is a period of approximately 223 synodic months (approximately 6,585.3211 days, or 18 years, 11 days, 8 hours), that can be used to predict eclipses of the Sun and Moon. One saros period after an eclipse, the Sun, Earth, and Moon return to approximately the same relative geometry, a near straight line, and a nearly identical eclipse will occur, in what is referred to as an eclipse cycle. A sar is one half of a saros. A series of eclipses that are separated by one saros is called a saros series.


In Other Number Systems

83 in Roman numerals is LXXXIII.

83 in binary (base 2) is 10100112.

83 in ternary (base 3) is 100023.

83 in quaternary (base 4) is 11034.

83 in quinary (base 5) is 3135.

83 in senary (base 6) is 2156.

83 in octal (base 8) is 1238.

83 in duodecimal (base 12) is 6B12.

83 in hexadecimal (base 16) is 5316.

83 in vigesimal (base 20) is 4320.

83 in base 36 is 2B36.


Mathematics

83 is both a Sophie Germain prime and a safe prime. A prime number p is a Sophie Germain prime if 2p + 1 is also prime. The number 2p + 1 associated with a Sophie Germain prime is called a safe prime.
As a Sophie Germain prime, 2 × 83 + 1 = 167 (167 is the safe prime).
As a safe prime, 2 × 41 + 1 = 83 (41 is the Sophie Germain prime)

83 is a Chen prime. A prime number p is called a Chen prime if p + 2 is either a prime or a product of two primes (also called a semiprime). The even number 2p + 2 therefore satisfies Chen’s theorem. The lower member of a pair of twin primes is by definition a Chen prime.

83 is an Eisenstein prime with no imaginary part and real part of the form 3n – 1. An Eisenstein prime is an Eisenstein integer

z = a + bω     (ω = e2πi/3)

that is irreducible (or equivalently prime) in the ring-theoretic sense: its only Eisenstein divisors are the units (±1, ±ω, ±ω2), a + bω itself and its associates. The associates (unit multiples) and the complex conjugate of any Eisenstein prime are also prime.

83 is a highly cototient number. A highly cototient number is a positive integer k which is above one and has more solutions to the equation

x – φ(x) = k,

than any other integer below k and above one. Here, φ is Euler’s totient function.


In Other Languages

In Afrikaans eighty-three is drie en tagtig.

In Albanian eighty-three is tetëdhjetë e tre.

In Amharic eighty-three is የሰማንያ ሦስት (_____).

In Arabic eighty-three is ثلاث وثمانون (thlath wathamanun).

In Armenian eighty-three is ութսուներեք (ut’sunerek’).

In Azerbaijani eighty-three is səksən üç.

In Basque eighty-three is laurogeita hiru.

In Belarusian eighty-three is восемдзесят тры (vosiemdziesiat try).

In Bengali eighty-three is তিরাশি (tirāśi).

In Bosnian eighty-three is osamdeset i tri.

In Bulgarian eighty-three is осемдесет и три (osemdeset i tri).

In Catalan eighty-three is vuitanta-tres.

In Cebuano eighty-three is kawaloan ug tulo ka.

In Cherokee eighty-three is ᏧᏁᎳᏍᎪ ᏦᎢ (tsunelasgo tsoi). More info.

In Chichewa eighty-three is eyite atatu.

In Chinese (Simplified) eighty-three is 八十三 (bāshísān).

In Chinese (Traditional) eighty-three is 八十三 (bāshísān).

In Corsican eighty-three is ottanta-di trè.

In Croatian eighty-three is osamdeset tri.

In Czech eighty-three is osmdesát tři.

In Danish eighty-three is treogfirs.

In Dutch eighty-three is drieëntachtig.

In Esperanto eighty-three is okdek tri.

In Estonian eighty-three is kaheksakümmend kolm.

In Filipino eighty-three is may walong pu’t tatlong.

In Finnish eighty-three is kahdeksankymmentäkolme.

In French eighty-three is quatre vingt trois.

In Frisian eighty-three is trijentachtich.

In Galician eighty-three is oitenta e tres.

In Georgian eighty-three is ოთხმოცდასამი (ot’khmots’dasami).

In German eighty-three is dreiundachtzig.

In Greek eighty-three is ογδόντα τρία (ogdónta tría).

In Gujarati eighty-three is એંસી ત્રણ (ēnsī traṇa).

In Haitian Creole eighty-three is katreven-twa.

In Hausa eighty-three is tamanin da uku.

In Hawaiian eighty-three is kanawalu-ekolu.

In Hebrew eighty-three is שמונים ושלוש (_____).

In Hindi eighty-three is तिरासी (tiraasee).

In Hmong eighty-three is eighty-peb.

In Hungarian eighty-three is nyolcvanhárom.

In Icelandic eighty-three is áttatíu og þrír. More info.

In Igbo eighty-three is iri-na-atọ.

In Indonesian eighty-three is delapan puluh tiga.

In Irish eighty-three is ochtó is trí.

In Italian eighty-three is ottantatre.

In Japanese eighty-three is 八十三 (yasomi).

In Javanese eighty-three is wolung puluh telu.

In Kannada eighty-three is ಎಂಬತ್ಮೂರು (embatmūru).

In Kazakh eighty-three is сексен үш (seksen üş).

In Khmer eighty-three is ប៉ែតសិប​បី (betseb​ bei).

In Korean eighty-three is 여든세 (yeodeunse).

In Kurdish (Kurmanji) eighty-three is heştê-sê.

In Kyrgyz eighty-three is сексен үч (seksen üç).

In Lao eighty-three is eighty ສາມ (eighty sam).

In Latin eighty-three is octoginta trium.

In Latvian eighty-three is astoņdesmit trīs.

In Lithuanian eighty-three is aštuoniasdešimt trys.

In Luxembourgish eighty-three is uechtzeg-dräi.

In Macedonian eighty-three is осумдесет и три (osumdeset i tri).

In Malagasy eighty-three is amby valo-telo.

In Malay eighty-three is lapan puluh tiga.

In Malayalam eighty-three is എണ്പത്തിമൂന്ന് (eṇpattimūnn).

In Maltese eighty-three is tlieta u tmenien (tlieta “three” u “and” tmenien “eighty”). More info.

In Maori eighty-three is e waru tekau-toru.

In Marathi eighty-three is त्र्याऐंशी (tryā’ainśī).

In Mongolian eighty-three is наян гурав (nayan gurav)

In Myanmar (Burmese) eighty-three is ရှစ်ဆယ့်သုံး (shit s y sone).

In Navajo eighty-three is tseebídiin dóó ba’ąą táá’ (tseebídiin “eighty” dóó ba’ąą “and in addition to it” táá’ “three”). More info.

In Nepali eighty-three is असी तीन (asī tīna).

In Norwegian eighty-three is åttitre.

In Pashto eighty-three is اتيا درې (_____).

In Persian eighty-three is هشتاد و سه (_____).

In Polish eighty-three is osiemdziesiąt trzy.

In Portuguese eighty-three is oitenta e três.

In Punjabi eighty-three is ਅੱਸੀ-ਤਿੰਨ (asī-tina).

In Romanian eighty-three is optzeci și trei.

In Russian eighty-three is восемьдесят три (vosem’desyat tri).

In Samoan eighty-three is valusefulu-tolu.

In Scots Gaelic eighty-three is ceithir fichead ’sa trì.

In Serbian eighty-three is осамдесет три (osamdeset tri).

In Sesotho eighty-three is mashome a robeli e meraro.

In Shona eighty-three is makumi masere nematatu.

In Sindhi eighty-three is اسي-ٽي (_____).

In Sinhala eighty-three is අසු තුන (asu tuna).

In Slovak eighty-three is osemdesiat tri.

In Slovenian eighty-three is tri in osemdeset.

In Somali eighty-three is siddeetan iyo saddex.

In Spanish eighty-three is ochenta y tres (ochenta “eighty” y “and” tres “three”).

In Sundanese eighty-three is dalapan puluh tilu.

In Swahili eighty-three is themanini na mitatu.

In Swedish eighty-three is _____.

In Tajik eighty-three is ҳаштоду се (_____).

In Tamil eighty-three is எண்பத்தி மூன்று (eṇpatti mūṉṟu).

In Telugu eighty-three is ఎనభై మూడు (enabhai mūḍu).

In Thai eighty-three is แปดสิบสาม (pæd s̄ib s̄ām).

In Turkish eighty-three is seksen üç.

In Ukrainian eighty-three is вісімдесят три (visimdesyat try).

In Urdu eighty-three is تراسی (_____).

In Uzbek eighty-three is sakson uch.

In Vietnamese eighty-three is tám mươi ba.

In Welsh eighty-three is wyth deg tri o.

In Xhosa eighty-three is asibhozo anesithathu.

In Yiddish eighty-three is _____ (_____). (אַכציק “eighty” דרײַ “three”). More info.

In Yoruba eighty-three is ọgọrin-mẹta.

In Zulu eighty-three is ayisishiyagalombili nantathu.