Recognised as Number
4,001
- Positive
- Odd
- Prime
- 4 digits
4,001 is an odd 4-digit integer and a prime number. It has 2 divisors and a digital root of 5.
Number properties
ParityOddnot divisible by 2
SignPositive
PrimalityPrime
Absolute value4,001
Digit count4
Digit sum5
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root5repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation4,001
Distinct prime factors14,001
Number of divisors2
Sum of divisors σ(n)4,002
Aliquot sum1sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)4,000integers below n that share no factor with it
Carmichael function λ(n)4,000the smallest exponent with aˣ ≡ 1 for every unit coprime to n
Möbius function μ(n)−11 distinct prime factor, an odd number of them
SquarefreeYesno repeated prime factor
All divisors1, 4,0012 in total
Arithmetic
Previous number4,000
Next number4,002
Double8,002
Half2,000.5
Square16,008,001
Cube64,048,012,001
Square root63.253458403≈irrational, shown to 9 decimal places
Cube root15.875333244≈
Negation-4,001
Reciprocal0.0002499375≈
Representations
Decimal4,001
Binary11111010000112 bits
Octal7641
HexadecimalFA1
Base 36335
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsfour thousand and one
Ordinalfour thousand and first
Scientific notation4.001 × 10^3
Engineering notation4.001 × 10^3
In other bases
Ternary12111012base 3; the most digit-efficient integer base after e: 8 digits
Quinary112001base 5; one hand: 6 digits
Septenary14444base 7: 5 digits
Nonary5435base 9; each digit is two ternary digits: 4 digits
Duodecimal2395base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits
Vigesimala01base 20; hands and feet, and the Mayan and Yoruba systems: 3 digits
Sexagesimal1:6:41base 60; Babylonian, and still how an hour and a circle are divided: 3 digits
Balanced ternary1TT1111TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1000011100001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
0000111110100001
Bit length12 bitsto write the magnitude
Set bits7the population count, or Hamming weight
Zero bits5within that length
Bit parityodd7 set bits, so odd; not the same as the number itself being odd
Highest set bitbit 11worth 2,048
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes20f a1
Gray code100001110001n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
16-bit0000111110100001
32-bit00000000000000000000111110100001
64-bit0000000000000000000000000000000000000000000000000000111110100001
One's complement1111000001011110at 16 bits, every bit flipped
Bits reversed1000010111110000at 16 bits
Rotated left by 10001111101000010at 16 bits, wrapping
Shifted left by 11111101000010= 8,002, no wrap
Shifted right by 111111010000= 2,000, discarding the low bit
These bits as a double1.97675665 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
4,001 to the power 216,008,001
4,001 to the power 364,048,012,001
4,001 to the power 4256,256,096,016,001
4,001 to the power 51,025,280,640,160,020,001
First ten multiples4,001, 8,002, 12,003, 16,004, 20,005, 24,006, 28,007, 32,008, 36,009, 40,010
Powers of twoBetween 2^11 (2,048) and 2^12 (4,096)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3No, remainder 2
Divisible by 4No, remainder 1
Divisible by 5No, remainder 1
Divisible by 6No, remainder 5
Divisible by 7No, remainder 4
Divisible by 8No, remainder 1
Divisible by 9No, remainder 5
Divisible by 10No, remainder 1
Divisible by 11No, remainder 8
Divisible by 12No, remainder 5
Divisible by 100No, remainder 1
Collatz (3n + 1) trajectory
Steps to reach 143the total stopping time
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps4,001 → 12,004 → 6,002 → 3,001 → 9,004 → 4,502 → 2,251 → 6,754 → 3,377 → 10,132 → …
Last steps… → 32 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage400,100%
4,001% as a decimal40.01
4,001% of 1004,001
4,001% of 1,00040,010
As a fraction of 1004,001/100
Read another way
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Derived from 4,001
Also reads as
4001 (year)
- Common year
- 365 days
- 41st century
- Ox
4001 will be a common year of 365 days. It begins on a Monday and ends on a Monday. Easter Sunday falls on 25 March.
Structure of the year
Patterns forced by the calendar
Weekday counts52 of each, plus an extra Monday365 days is 52 weeks and 1 day, and the remainder starts on the weekday 1 January falls on
Sundays52
Mondays53one of the extras
Tuesdays52
Wednesdays52
Thursdays52
Fridays52
Saturdays52
Friday the 13th2 of them13 April, 13 July
ISO weeks52an ordinary 52-week year
Same calendar as3990the most recent year whose calendar is identical, so a printed one could be reused
Calendar repeats in4007, 4018, 40296 years later, then again after that; the gap is 6, 11 or 28 years, broken by centuries that skip a leap year
Months of 4001
January31 days, starts Monday
February28 days, starts Thursday
September30 days, starts Saturday
October31 days, starts Monday
November30 days, starts Thursday
December31 days, starts Saturday
Time references
These values depend on today’s date and change daily.
Unix timestamp at the start64,092,211,200
Unix timestamp at the end64,123,747,199
Years from now1,975 years from now
Days from today721,097 days to 1 January
The number 4001
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Also reads as
#440000 (colour)
- #440000
- Red
- Dark
- Nearest: Maroon
#440000 is a red with RGB values 68, 0, 0 and HSL 0°, 100%, 13%. It is a dark colour, so white text on it reaches 16.9:1 contrast (AAA for normal text). The nearest named colour is Maroon.
Colour values
#440000#440000
HEX#440000
HEX (short)#400
RGBrgb(68, 0, 0)
RGB (0–1)0.2667, 0, 0
RGB percentages26.7%, 0%, 0%
HSLhsl(0, 100%, 13.3%)
HSV / HSBhsv(0, 100%, 26.7%)
CMYK0%, 100%, 100%, 73.3%≈naive device-independent conversion; real print needs an ICC profile
24-bit integer4,456,448
CSS custom property--colour: #440000;
Brightness & contrast
Relative luminance0.01229WCAG 2.x, 0 is black and 1 is white
Perceived brightness37.2 of 255ITU-R BT.601 weighting
Light or darkDark
Best text colour on this backgroundWhitecontrast 16.86:1
Contrast with white16.86:1WCAG normal text: AAA
Contrast with black1.25:1WCAG normal text: Fail
Greyscale equivalent#0E0E0E
Inverted#BBFFFF
Colour vision & accessibility
Distinguishable without hueShifts in lightness toonever rely on hue alone to carry meaning
Contrast with white, large text16.86:1WCAG large text: AAA
Contrast with black, large text1.25:1WCAG large text: Fail
Named colours
Hue familyred
CSS keyword usableNo exact keyword
Colour harmonies
Complementary#004444
Analogous#440022, #442200
Triadic#004400, #000044
Split complementary#004422, #002244
Tetradic#224400, #004444, #220044
Tints, shades & saturation
Channel breakdown
R68
G0
B0
Red68 (26.7%)
Green0 (0%)
Blue0 (0%)
Hue0°
Saturation (HSL)100%
Lightness13.33%
Dominant channelRed
Hex per channelR 44 · G 00 · B 00
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