Numbers 10,000,000,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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10,000,000,000,037

[Math.]  The smallest 14-digit prime number.

10,999,999,999,989 & 32,999,999,999,967 & 98,999,999,999,901

[Math.]

(*)   332×9 = 1089×9 = 9,801 = 992 & 1089×9801 = 10,673,289 = 32672

1089…1089×9 = 9801…9801  & 1089…1089×9801…9801  = 3267…32672

(**)  10989×9 = 98901 & 10989×98901 = 1,086,823,089 = 329672

10989…10989×9 = 98901…98901 & 10989…10989×98901...98901 = 32967…329672

...

(***)   10,999,999,999,989×9 = 98,999,999,999,901 &

10,999,999,999,989×98,999,999,999,901 = 32,999,999,999,9672

1099999999989…109999999989×9 = 9899999999901…9899999999901 &

1099999999989…1099999999989×9899999999901...9899999999901 =

= 32999999967…32999999999672

...

(****)  109…989×9 = 989…901 & 109...989×989…901 = 329…9672

109…989...109…989×9 = 989…901...989…901  &

109…989…109…989×989…901...989…901 = 329…967…329…9672.

11,111,111,111,111

[Math.]

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

11111111111×11111111111 = 123456790120987654321

11,223,344,332,211

[Math.]

11×11 = 121;

112211×11 = 1,234,321

1122332211×11 = 12,345,654,321

11223344332211×11 = 123,456,787,654,321

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

…

12,345,678,901,234 & 98,765,432,109,876

[Math.]

1×8+1 = 9

12×8+2 = 98

123×8+3 = 987

1234×8+4 = 9876

12,345×8+5 = 98,765

123,456×8+6 = 987,654

1,234,567×8+7 = 9,876,543

12,345,678×8+8 = 98,765,432

123,456,789×8+9 = 987,654,321

1,234,567,890×8+90 = 9,876,543,210

(Start of new cycle)

12,345,678,901×8+901 = 98,765,432,109

123,456,789,012×8+9002 = 987,654,321,098

1,234,567,890,123×8+90,003 = 9,876,543,210,987

12,345,678,901,234×8+900,004 = 98,765,432,109,876

123,456,789,012,345×8+9,000,005 = 987,654,321,098,765

1,234,567,890,123,456×8+90,000,006 = 9,876,543,210,987,654

12,345,678,901,234,567×8+900,000,007 = 98,765,432,109,876,543

123,456,789,012,345,678×8+9,000,000,008 = 987,654,321,098,765,432

1,234,567,890,123,456,789×8+90,000,000,009 = 9,876,543,210,987,654,321

12,345,678,901,234,567,890×8+ 900,000,000,090 = 98,765,432,109,876,543,210

(end of cycle)

13,689,992,600,001 & 36,999,999,999,999 & 33,669,999,999,999

[Math.] (See below)

14,285,714,285,714

[Math.]

1×7 + 3 = 10

14×7 + 2 = 100

142×7 + 6 = 1000

1428×7 + 4 = 10000

14285×7 + 5 = 100000

142857×7 + 1 = 1000000

1428571×7 + 3 = 10000000

14285714×7 + 2 = 100000000

142857142×7 + 6 = 1000000000

1428571428×7 + 4 = 10000000000

14285714285×7 + 5 = 100000000000

142857142857×7 + 1 = 1000000000000

1428571428571×7 + 3 = 10000000000000

14285714285714×7 + 2 = 100000000000000

142857142857142×7 + 6 = 1000000000000000

1428571428571428×7 + 4 = 10000000000000000

14285714285714285×7 + 5 = 100000000000000000

142857142857142857×7 + 1 = 1000000000000000000

15,999,999,999,984 & 27,999,999,999,972 & 48,999,999,999,951

[Math.]

7,683,984 = 1584×4851 = 27722

782,432,784 = 15984×48951 = 279722

78,384,320,784 = 159984×489951 = 2799722

7,839,843,200,784 = 1599984×4899951 = 27999722

783,998,432,000,784 = 15999984×48999951 = 279999722

78,399,984,320,000,784 = 159999984×489999951 = 2799999722

7,839,999,843,200,000,784 = 1599999984×4899999951 = 27999999722

783,999,998,432,000,000,784 = 15999999984×48999999951 = 279999999722

78,399,999,984,320,000,000,784 = 159999999984×489999999951 = 2799999999722

7839…9984320000784 = 159…999984×489…999951 = 279…9999722.

19,359,612,801,936 & 21,999,999,999,978 &

43,999,999,999,956 & 87,999,999,999,912

[Math.]

(*)   8712 = 2178×4 & 8712×2178 = 18,974,736 = 43562

87128712 = 21782178×4 & 87128712×21782178 = 435643562

(**)   87912 = 21978×4 & 21978×87912 = 1,932,129,936 = 439562

8791287912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…439562

...

(***)   8799912 = 2199978×4 & 2199978×8799912 = 19,359,612,801,936 = 43999562

87999128799912 = 21999782199978×4 &

21999782199978×87999128799912 = 439995643999562

...

(***)   87,999,999,999,912 = 21,999,999,999,978×4 &

21,999,999,999,978×87,999,999,999,912 = 43,999,999,999,9562

8799...99128799...9912 = 2199...99782199...9978×4 &

2199...99782199...9978×8799...99128799...9912 = 4399...99564399...99562

...

(****)   879…912 = 219…978×4 & 219…978×879…912 = 439…9562

879…912879…912 = 219…978…219…978×4 &

219…978219…978×879...912…879...912 = 439…956439…9562.

30.861…×1012

[Astronomy]  The approximate length (km, kilometers) of a parsec (parallax second), the distance from the Sun that would be a second of arc as observed from the Earth. 1 parsec = 3.262 light years.

31.536×1012

[EECS] A 1-MIPS year is equivalent to the computing power of a MIPS computer running for one year = 31.536×1012 arithmetic operations. MIPS = million instructions per second, for measuring speeds of microprocessors.

10,999,999,999,989 & 32,999,999,999,967 & 98,999,999,999,901

(See more above)

33,333,333,333,333 & 33,333,336,666,667

[Math.]

3×37 = 111

33×3367 = 111,111

333×333667 = 111,111,111

3333×33336667 = 111,111,111,111

33333×3333366667 = 111,111,111,111,111

333333×333333666667 = 111,111,111,111,111,111

3333333×33333336666667 = 111,111,111,111,111,111,111

33333333×3333333366666667 = 111,111,111,111,111,111,111,111

333333333×333333333666666667 = 111,111,111,111,111,111,111,111,111

3333333333×33333333336666666667 = 111,111,111,111,111,111,111,111,111,111

33333333333×3333333333366666666667 =

= 111,111,111,111,111,111,111,111,111,111,111

333333333333×333333333333666666666667 =

= 111,111,111,111,111,111,111,111,111,111,111,111

3333333333333×33333333333336666666666667 =

= 111,111,111,111,111,111,111,111,111,111,111,111,111

33,333,333,333,333×3333333333333366666666666667 =

= 111,111,111,111,111,111,111,111,111,111,111,111,111,111

...

29,999,999,999,996 & 33,333,336,666,667 99,987,666,543,332

[Math.]

296×333,667 = 98,765,432

2,996×33,336,667 = 99,876,654,332

29,996×3,333,366,667 = 99,987,666,543,332

299,996×333,333,666,667 = 99,998,766,665,433,332

2,999,996×33,333,336,666,667 = 99,999,876,666,654,333,332

29,999,996×3,333,333,366,666,667 = 99,999,987,666,666,543,333,332

299,999,996×333,333,333,666,666,667 = 99,999,998,766,666,665,433,333,332

2,999,999,996×33,333,333,336,666,666,667 = 99,999,999,876,666,666,654,333,333,332

29,999,999,996×3,333,333,333,366,666,666,667 =

= 99,999,999,998,766,666,666,663,333,333,332

299,999,999,996×333,333,333,333,366,666,666,667 =

= 99,999,999,998,766,666,666,665,433,333,333,332

...

33,333,336,666,667

[Math.]

372 = 1369 = 1368+1;

33672 = 11336689 = 11336688+1

333,6672 = 111,333,666,889 = 111,333,666,888+1

333366672 = 1111333366668889 = 1111333366668888+1

33333666672 = 11111333336666688889 = 11111333336666688888+

3333336666672 = 111111333333666666888889 = 111111333333666666888888+1

333333366666672 =

= 1111111333333366666668888889 = 1111111333333366666668888888+1

13,689,992,600,001 & 36,999,999,999,999 & 33,669,999,999,999

[Math.]

3692 = 136,161

36992 = 13682601

36,9992 = 1368926001

369,9992 = 136899260001

3,699,9992 = 13689992600001

36,999,9992 = 1368999926000001

369,999,9992 = 136899999260000001

3,699,999,9992 = 13689999992600000001

36,999,999,9992 = 1368999999926000000001

369,999,999,9992 = 136899999999260000000001

3366992 = 113366,216601

336699992 = 11336688,32660001

33669999992 = 1133668899,3266000001

3366999999992 = 113366889999,326600000001

333,666,9992 = 111,333,666,221,666,001

333,666,999,9992 = 111,333,666,888,332,666,000,001

333,666,999,999,9992 = 111,333,666,888,999,332,666,000,000,001

3333,6666,99992 = 1111,3333,6666,2221,6666,0001

3333,6666,9999,99992 = 1111,3333,6666,8888,3332,6666,0000,0001

36,361,380,737,780 &  36,361,380,737,781 & 51,422,757,785,981

[Math.]  The 18th square number that is the sum of squares of 2 consecutive numbers: 51,422,757,785,9812+51,422,757,785,9812= 51,422,757,785,9812. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 52, 292, 1692, 9852

Or in other words: (36,361,380,737,780, 36,361,380,737,781, 51,422,757,785,981) is the 18th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

43,520,999,798,747

[Math.] The 50th Keith number: 43,520,999,798,747.

43,892,069,261,881

[Math.]  The 9th square number that is the sum of squares of 2 consecutive numbers: 6,625,1092 = 43,892,069,261,881 = 4,684,6592+4,684,6602. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 52, 292, 1692, 9852

Or in other words:

(4,684,659, 4,684,660, 6,625,109) is the 9th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

44,444,440,000,000 & 66,666,666,666,666.333333333333332

[Math.]  The square root of the number formed by n digits 4 followed by n digits 0 starts with n digits 6, decimal point, and n digits 3:

401/2 = 6.32…

44001/2 = 66.332…

4440001/2 = 666.3332…

444400001/2 = 6666.33332…

44444000001/2 = 66666.333332…

4444440000001/2 = 666666.3333332…

444444400000001/2 = 6666666.33333332…

44444444000000001/2 = 66666666.333333332…

4444444440000000001/2 = 666666666.3333333332…

44444444440000000001/2 = 6666666666.33333333332…

4444444444400000000001/2 = 66666666666.333333333332…

444444444444000000000001/2 = 666666666666.3333333333332…

44444444444440000000000001/2 = 6666666666666.33333333333332…

4444444444444400000000000001/2 = 66666666666666.333333333333332…

444444444444444000000000000001/2 = 666666666666666.3333333333333332…

44444444444444440000000000000001/2 = 6666666666666666.33333333333333332…

51,422,757,785,981

(Above)

60,493,815,061,729

[Math.]

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.

61,728,399,382,716

Math.]

 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.

66,666,663,333,334

[Math.]

642 = 4096 = 4095+1

66342 = 44009956 = 44009955+1

666,3342 = 444,000,999,556 = 444,000,999,555+1

666633342 = 4444000099995556 = 4444000099995555+1

66666333342 = 44444000009999955556 =  44444000009999955555+1

6666663333342 = 444444000000999999555556 = 444444000000999999555555+1.

666666633333342

= 4444444000000099999995555556 = 4444444000000099999995555555+1.

74,596,893,730,427

[Math.]  A prime number. The 51st Keith number: 74,596,893,730,427.

77,111,111,111,117 & 88,888,888,888,888

[Math.]

8×8+13 = 77

88×8+13 = 717

888×8+13 = 7117

8888×8+13 = 71117

88,888×8+13 = 711,117

888,888×8+13 = 7,111,117

8,888,888×8+13 = 71,111,117

88,888,888×8+13 = 711,111,117

888,888,888×8+13 = 7,111,111,117

8,888,888,888×8+13 = 71,111,111,117

88,888,888,888×8+13 = 711,111,111,117

888,888,888,888×8+13 = 7,111,111,111,117

8,888,888,888,888×8+13 = 77,111,111,111,117

88,888,888,888,888×8+13 = 777,111,111,111,117

...

88,888,888,888,888 & 98,765,432,098,766

[Math.]

9×9+(9–2) = 88

98×9+(9–3) = 888

987×9+(9–4) = 8,888

9,876×9+(9–5) = 88,888

98,765×9+(9–6) = 888,888

987,654×9+(9–7) = 8,888,888

9,876,543×9+(9–8) = 88,888,888

98,765,432×9+(9–9) = 888,888,888

987,654,321×9+(9–10) = 8,888,888,888

9,876,543,210×9+(9–11) = 88,888,888,888

98,765,432,099×9+(9–12) = 888,888,888,888  = 98,765,432,100×9–12.

987,654,320,988×9+(9–13) = 8,888,888,888,888

9,876,543,209,877×9+(9–14) = 88,888,888,888,888

98,765,432,098,766×9+(9–15) = 888,888,888,888,888

987,654,320,987,655×9+(9–16) = 8,888,888,888,888,888

9,876,543,209,876,544×9+(9–17) = 88,888,888,888,888,888

...

97,295,849,958,669

[Math.]  The 52nd Keith number: 97,295,849,958,669.

98,765,432,098,766

[Math.]

9×9+(9–2) = 88

98×9+(9–3) = 888

987×9+(9–4) = 8,888

9,876×9+(9–5) = 88,888

98,765×9+(9–6) = 888,888

987,654×9+(9–7) = 8,888,888

9,876,543×9+(9–8) = 88,888,888

98,765,432×9+(9–9) = 888,888,888

987,654,321×9+(9–10) = 8,888,888,888

9,876,543,210×9+(9–11) = 88,888,888,888

98,765,432,099×9+(9–12) = 888,888,888,888  = 98,765,432,100×9–12.

987,654,320,988×9+(9–13) = 8,888,888,888,888

9,876,543,209,877×9+(9–14) = 88,888,888,888,888

98,765,432,098,766×9+(9–15) = 888,888,888,888,888

987,654,320,987,655×9+(9–16) = 8,888,888,888,888,888

9,876,543,209,876,544×9+(9–17) = 88,888,888,888,888,888

...

10,999,999,999,989 & 32,999,999,999,967 & 98,999,999,999,901

[Math.] (See more above)

29,999,999,999,996 & 33,333,336,666,667 &  99,987,666,543,332

[Math.]

296×333,667 = 98,765,432

2,996×33,336,667 = 99,876,654,332

29,996×3,333,366,667 = 99,987,666,543,332

299,996×333,333,666,667 = 99,998,766,665,433,332

2,999,996×33,333,336,666,667 = 99,999,876,666,654,333,332

29,999,996×3,333,333,366,666,667 = 99,999,987,666,666,543,333,332

299,999,996×333,333,333,666,666,667 = 99,999,998,766,666,665,433,333,332

2,999,999,996×33,333,333,336,666,666,667 =

99,999,999,876,666,666,654,333,333,332

29,999,999,996×3,333,333,333,366,666,666,667 =

= 99,999,999,998,766,666,666,663,333,333,332

299,999,999,996×333,333,333,333,366,666,666,667 =

= 99,999,999,998,766,666,666,665,433,333,333,332

...

99,999,999,999,973

[Math.]  The largest 14-digit prime number = 99,999,999,999,973.