Recognised as Number

1,998,413

Positive
Odd
Prime
7 digits

1,998,413 is an odd 7-digit integer and a prime number. It has 2 divisors and a digital root of 8.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value1,998,413

Digit count7

Digit sum35

Digit product7,776

Multiplicative persistence3times the digit product can be taken before one digit is left

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation1,998,413

Distinct prime factors11,998,413

Number of divisors2

Sum of divisors σ(n)1,998,414

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)1,998,412integers below n that share no factor with it

Carmichael function λ(n)1,998,412the 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, 1,998,4132 in total

Arithmetic

Previous number1,998,412

Next number1,998,414

Double3,996,826

Half999,206.5

Square3,993,654,518,569

Cube7,980,971,107,417,030,997

Square root1,413.652361792≈irrational, shown to 9 decimal places

Cube root125.958771259≈

Negation-1,998,413

Reciprocal5.00397065 × 10^-7≈

Representations

Decimal1,998,413

Binary11110011111100100110121 bits

Octal7477115

Hexadecimal1E7E4D

Base 3616TZH

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

In wordsone million, nine hundred and ninety-eight thousand, four hundred and thirteen

Ordinalone million, nine hundred and ninety-eight thousand, four hundred and thirteenth

Scientific notation1.998413 × 10^6

Engineering notation1.998413 × 10^6

In other bases

Ternary10202112022022base 3; the most digit-efficient integer base after e: 14 digits

Quinary1002422123base 5; one hand: 10 digits

Septenary22662164base 7: 8 digits

Nonary3675268base 9; each digit is two ternary digits: 7 digits

Duodecimal8045a5base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimalc9g0dbase 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal9:15:6:53base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary11T10TTT10T10Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111000001001011101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000111100111111001001101

Bit length21 bitsto write the magnitude

Set bits14the population count, or Hamming weight

Zero bits7within that length

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

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes31e 7e 4d

Gray code100010100000101101011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000111100111111001001101

64-bit0000000000000000000000000000000000000000000111100111111001001101

One's complement11111111111000011000000110110010at 32 bits, every bit flipped

Bits reversed10110010011111100111100000000000at 32 bits

Rotated left by 100000000001111001111110010011010at 32 bits, wrapping

Shifted left by 11111001111110010011010= 3,996,826, no wrap

Shifted right by 111110011111100100110= 999,206, discarding the low bit

These bits as a double9.8734721 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,998,427+14

Previous prime1,998,397−16

Distance to nearest prime0, it is prime

Nearest square below1,996,569

Nearest square above1,999,396

Powers & multiples

1,998,413 to the power 23,993,654,518,569

1,998,413 to the power 37,980,971,107,417,030,997

1,998,413 to the power 415,949,276,413,686,591,165,807,761

1,998,413 to the power 531,873,241,325,704,661,711,435,385,083,293

First ten multiples1,998,413, 3,996,826, 5,995,239, 7,993,652, 9,992,065, 11,990,478, 13,988,891, 15,987,304, 17,985,717, 19,984,130

Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 4

Divisible by 8No, remainder 5

Divisible by 9No, remainder 8

Divisible by 10No, remainder 3

Divisible by 11No, remainder 10

Divisible by 12No, remainder 5

Divisible by 100No, remainder 13

Collatz (3n + 1) trajectory

Steps to reach 1114the total stopping time

Highest value reached5,995,2403× the starting value

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

First steps1,998,413 → 5,995,240 → 2,997,620 → 1,498,810 → 749,405 → 2,248,216 → 1,124,108 → 562,054 → 281,027 → 843,082 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage199,841,300%

1,998,413% as a decimal19,984.13

1,998,413% of 1001,998,413

1,998,413% of 1,00019,984,130

As a fraction of 1001,998,413/100

Read another way

As seconds23 days, 3 hours and 6 minutes

As bytes1.906 MiB

As a 24-bit colour#1E7E4D

Keep nerding

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