Numbers 710,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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710,647

[Math.]  The 28th Lucas number.

 

711,117

[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

...

 

712,216

[Math.]  A pair of amicable numbers (635624, 712216).

 

714,285

[Math.]  The 6-digit period of the rational number 1/7 = 0.142857142857… or 0.142857. Its multiple by 7 is 999,999.  Then,   142,857×n = abc,def,ghi,jkl and

abc,def+ghi,jkl = 142,857, if n  = 7t+1

abc,def+ghi,jkl = 571,428, if n  = 7t+4

abc,def+ghi,jkl = 285,714, if n  = 7t+2

abc,def+ghi,jkl = 714,285, if n  = 7t+5

abc,def+ghi,jkl = 428,571, if n  = 7t+3

abc,def+ghi,jkl = 857,142, if n  = 7t+6,

for t = 0 to 142,856, and in fact abc,edf = t. The results are digit-rotations of 142,857 and the sums of first and last 3-digit numbers are always 999.

 

[Math.]  142,857×5 = 714,285 = 8572–1422, where 857,142 = 142,857×6.

 

715,716

[Math.]  A square number 8462 = 715,716, formed by concatenation of 2 consecutive numbers.

 

716,895

[Math.]  Two consecutive sums of consecutive numbers:

7921+…+8010 = 8011+…+8099 = 716,895.  

 

717,948

[Math.]  179,487×4 = 717,948.

 

718,751

[Math.]  Its odd powers end with 718,751. Its even powers end with 000,001.

 

719,333

[Math.]  A right-truncatable prime number: self, 71933, 7193, 719, 71 and 7 are prime numbers.