Number 11 in Math

A page of the Numeropedia - the Special Encyclopedia of Numbers

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The smallest 2-digit prime number.

An absolute prime number (or permutable prime number).

The only palindromic prime number of even number of digits is 11. (A palindromic number of even number of digits must be divisible by 11, hence, it is not prime).

The 5th prime number is 11. The second known case that both those numbers are palindromic prime numbers is: the 8,114,118th prime number is 143,787,341.

The only known 7 prime numbers consisting of the repeated digits 1 are the numbers of 2, 19, 23, 317, 1031, 49,081 and 86,453 digits 1.

652–562 = 332, 65+56 = 112 and 65–56 = 32.

1,010,101 = 101×10001 and 11,111,111 = 11×101×10001.

The product of the first 8 consecutive prime numbers, divided by 10:  2×3×5×7×11×13×17×19/10 = 969,969 is a palindromic number.

510,510 is the product of first 7 prime numbers, of 2 consecutive numbers and of 4 consecutive Fibonacci numbers: 510,510 = 2×3×5×7×11×13×17 = 714×715 = 13×21×34×55.

Repeatedly inserting numbers 36 in the middle of the prime number 11 yields other prime numbers: 1361, 136,361, 13,636,361, 1,363,636,361 and 136,363,636,361.

112 = 121 = 30+31+32+33+34.

The only other case: 400 = 202 = 70+71+72+73.

23+42+56 = 65+24+32 = 121 = 112 and

234,256 = (2+3+4+2+5+6)4 = 224.

 The 11th triangle number is 66 The 1111th triangle number is 617,716 The 111,111th triangle number is 6,172,882,716 The 11,111,111th triangle number is 61,728,399,382,716

All numbers are palindromic.

121 = 112

121×(1+2+1) = 484 = 222

12,321×(1+2+3+2+1) = 110,889 = 3332

1,234,321×(1+2+3+4+3+2+1) = 19,749,136 = 4,4442

123,454,321×(1+2+3+4+5+4+3+2+1) = 3,086,358,025 = 55,5552

12,345,654,321×(1+2+3+4+5+6+5+4+3+2+1) = 444,443,555,556 = 666,6662

1,234,567,654,321×(1+2+3+4+5+6+7+6+5+4+3+2+1) =

= 60,493,815,061,729 = 7,777,7772

123,456,787,654,321×(1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) =

= 7,901,234,409,876,544 = 88,888,8882

12,345,678,987,654,321×(1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1)

= 999,999,998,000,000,001 = 999,999,9992.

11×11 = 121

112,211×11 = 1,234,321

1,122,332,211×11 = 12,345,654,321

11,223,344,332,211×11 =  123,456,787,654,321

112,233,445,544,332,211×11  = 1,234,567,900,987,654,321

1×9+2 = 11

12×9+3 = 111

123×9+4 = 1,111

1234×9+5 = 11,111

12,345×9+6 = 111,111

123,456×9+7 = 1,111,111

1,234,567×9+8 = 11,111,111

12,345,678×9+9 = 111,111,111

123,456,789×9+10 = 1,111,111,111

1,234,567,900×9+11 = 11,111,111,111

...

1,001 = 11×91

1,000,001 = 101×9901

1,000,000,001 = 1001×999,001

1,000,000,000,001 = 10001×99,990,001

1,000,000,000,000,001 = 100001×9,999,900,001

99,889×11+(11–1) = 1,098,789

998,877,889×11+(11–1) = 10,987,656,789

9,988,776,677,889×11+(11–1) = 109,876,543,456,789

99887766556677889×11+(11–1) = 1,098,765,432,123,456,789

...

112 = 121 = (12–1)2

113 = 1331 = (13–3+1)3

114 = 14641 = (14–6+4–1)4

115 = 161,051 = (16–1+0–5+1)5

116 = 1,771,561 = (17–7+1–5+6–1)6

117 = 19,487,171 = (19–4+8–7+1–7+1)7

119 = 2,357,947,691 = (23–5+7–9+4–7+6–9+1)9

1110 = 25,937,424,601 = (25–9+3–7+4–2+4–6+0–1)10

118 = 214,358,881 and 21–4+3–5+8–8+8–1 = 22 = 11×2.

1×1 = 1

11×11 = 121

111×111 = 12321

1111×1111 = 1234321

11111×11111 = 123454321

111111×111111 = 12345654321

1111111×1111111 = 1234567654321

11111111×11111111 = 123456787654321

111111111×111111111 = 12345678987654321

1111111111×1111111111 = 1234567900987654321.

The 5th Lucas number.

A supersingular prime numbers factors of the order of the Monster group M:

246×320×59×76×112×133×17×19×23×29×31×41×47×59×71 =

=  808017424794512875886459904961710757005754368000000000.

The imaginary quadratic fields Q((–11)1/2) is one of only 9 UFDs (unique factorization domains) of form Q((–d)1/2), d = 1, 2, 3, 7, 11, 19, 43, 67 and 163.