Recognised as Number

7,001,003

Positive
Odd
Prime
7 digits

7,001,003 is an odd 7-digit integer and a prime number. It has 2 divisors and a digital root of 2.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value7,001,003

Digit count7

Digit sum11

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation7,001,003

Distinct prime factors17,001,003

Number of divisors2

Sum of divisors σ(n)7,001,004

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)7,001,002integers below n that share no factor with it

Carmichael function λ(n)7,001,002the 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, 7,001,0032 in total

Arithmetic

Previous number7,001,002

Next number7,001,004

Double14,002,006

Half3,500,501.5

Square49,014,043,006,009

Cube343,147,462,127,198,027,027

Square root2,645.940853458≈irrational, shown to 9 decimal places

Cube root191.302254365≈

Negation-7,001,003

Reciprocal1.42836676 × 10^-7≈

Representations

Decimal7,001,003

Binary1101010110100111010101123 bits

Octal32551653

Hexadecimal6AD3AB

Base 364620B

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsseven million, one thousand and three

Ordinalseven million, one thousand and third

Scientific notation7.001003 × 10^6

Engineering notation7.001003 × 10^6

In other bases

Ternary111011200120102base 3; the most digit-efficient integer base after e: 15 digits

Quinary3243013003base 5; one hand: 10 digits

Septenary113336042base 7: 9 digits

Nonary14150512base 9; each digit is two ternary digits: 8 digits

Duodecimal241760bbase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits

Vigesimal23f2a3base 20; hands and feet, and the Mayan and Yoruba systems: 6 digits

Sexagesimal32:24:43:23base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1111TTT01TT011Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1101111111101010011111111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000011010101101001110101011

Bit length23 bitsto write the magnitude

Set bits14the population count, or Hamming weight

Zero bits9within that length

Bit parityeven14 set bits, so even; not the same as the number itself being odd

Highest set bitbit 22worth 4,194,304

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes36a d3 ab

Gray code10111111011101001111110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000011010101101001110101011

64-bit0000000000000000000000000000000000000000011010101101001110101011

One's complement11111111100101010010110001010100at 32 bits, every bit flipped

Bits reversed11010101110010110101011000000000at 32 bits

Rotated left by 100000000110101011010011101010110at 32 bits, wrapping

Shifted left by 1110101011010011101010110= 14,002,006, no wrap

Shifted right by 11101010110100111010101= 3,500,501, discarding the low bit

These bits as a double3.45895507 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime7,001,011+8

Previous prime7,000,969−34

Distance to nearest prime0, it is prime

Nearest square below6,996,025

Nearest square above7,001,316

Powers & multiples

7,001,003 to the power 249,014,043,006,009

7,001,003 to the power 3343,147,462,127,198,027,027

7,001,003 to the power 42,402,376,411,794,899,768,810,108,081

7,001,003 to the power 516,819,044,466,105,328,666,138,873,105,405,243

First ten multiples7,001,003, 14,002,006, 21,003,009, 28,004,012, 35,005,015, 42,006,018, 49,007,021, 56,008,024, 63,009,027, 70,010,030

Powers of twoBetween 2^22 (4,194,304) and 2^23 (8,388,608)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 3

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 2

Divisible by 8No, remainder 3

Divisible by 9No, remainder 2

Divisible by 10No, remainder 3

Divisible by 11No, remainder 9

Divisible by 12No, remainder 11

Divisible by 100No, remainder 3

Collatz (3n + 1) trajectory

Steps to reach 1129the total stopping time

Highest value reached31,504,5164× the starting value

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps7,001,003 → 21,003,010 → 10,501,505 → 31,504,516 → 15,752,258 → 7,876,129 → 23,628,388 → 11,814,194 → 5,907,097 → 17,721,292 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage700,100,300%

7,001,003% as a decimal70,010.03

7,001,003% of 1007,001,003

7,001,003% of 1,00070,010,030

As a fraction of 1007,001,003/100

Read another way

As seconds81 days, 43 minutes and 23 seconds

As bytes6.677 MiB

As a 24-bit colour#6AD3AB

Keep nerding

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