61

61
Basic Information
Cardinal Number	sixty-one
Ordinal Number	sixty first
Roman Numeral	LXI
Greek Numeral	ΞΑ´
Factorization	61
Standard Form	6.1 × 101
Different Representations
Binary Form	1111012
Ternary Form	20213
Quaternary Form	3314
Quinary Form	2215
Senary Form	1416
Septenary Form	1157
Octal Form	758
Nonary Form	679
Undecimal Form	5611
Duodecimal Form	5112
Tridecimal Form	4913
Quattuordecimal Form	4514
Quindecimal Form	4115
Hexadecimal Form	3D16
Septendecimal Form	3A17
Octodecimal Form	3718
Novemdecimal Form	3419
Vigesimal Form	3120
Unvigesimal Form	2J21
Duovigesimal Form	2H22
Trevigesimal Form	2F23
Quattuorvigesimal Form	2D24
Quinvigesimal Form	2B25
Hexavigesimal Form	2926
Septenvigesimal Form	2727
Octovigesimal Form	2528
Novemvigesimal Form	2329
Trigesimal Form	2130
Untrigesimal Form	1U31
Duotrigesimal Form	1T32
Tretrigesimal Form	1S33
Quattuortrigesimal Form	1R34
Quintrigesimal Form	1Q35
Hexatrigesimal Form	1P36
Previous	59
Current	61
Next	67

61 is a prime number from 1-100. 61 has 2 factors, 1 and 61. It is the eighteenth prime number, and the eighteenth prime number from 1 to 100.

Proofs

• — 61 is divisible by 1.

• — 61 is not divisible by 2-60.

• — 61 is divisible by 61.

Therefore, 61 has two factors and is prime.

As an Exponent of Mersenne Number

2⁶¹ - 1, which is the number 2,305,843,009,213,693,951, is a prime number. It is the 9th Mersenne prime.

Relationship with other odd numbers

The numbers before

• 53 is the second previous prime number.
• 55 is a composite number. Its prime factorization is 5 * 11.
• 57 is also a composite number. Its prime factorization is 3 * 19.
• 59 is the previous odd number, as well as the previous prime number.
  • The difference between 61 and 59 is 2. Therefore, they are twin primes.

The numbers after

• The next odd number, 63, is a composite number. Its prime factorization is 3² * 7.
• 65 is also a composite number. Its prime factorization is 5 * 13.
• 67 is the next prime number.
  • The difference between 67 and 61 is 6. Therefore, they are sexy primes.

In science

• 61 is the atomic number of promethium.

Trivia

• 61 is a centered square number, since it is the sum of two consecutive squares, equal to $5^{2}+6^{2}.$
  • Additionally, 61 is a centered decagonal number and a centered hexagonal number.
• 61 is a Pillai prime, since 8! + 1 is divisible by 61, but 61 is not one more than a multiple of 8.
• 61 is the fourth cuban prime of the form ${\frac {x^{3}-y^{3}}{x-y}}$ where $x=y+1.$
• 61 is the largest prime factor of the Descartes number $198585576189=3^{2}\times 7^{2}\times 11^{2}\times 13^{2}\times 19^{2}\times 61,$ which would be the first odd perfect number discovered if 22,021, one of its composite factors, were prime.
• 61 is a prime number that becomes divisible by 7 if a 1 is inserted to the left of it, since ${\frac {161}{7}}=23.$

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Prime Numbers 1-1,000