**31,018,606,641**

[Math.] Sum of the first 593 cube numbers:

1^{3}+…+593^{3} = 31,018,606,641 = (1+…+593)^{2} = 176,121^{2}.

**31,228,191,225 **

[Math.] Sum of the first 594 cube numbers:

1^{3}+…+594^{3} = 31,228,191,225 = (1+…+594)^{2} = 176,715^{2}.

**31,381,886,305 **

[Math.] 31,381,886,305 = 1^{2}+3^{3}+5^{5}+7^{7}+9^{11}.

**31,438,836,100**

[Math.] Sum of the first 595 cube numbers:

1^{3}+…+595^{3} = 31,438,836,100** **= (1+…+595)^{2} = 177,310^{2}.

**31,509,019,100 **& **31,509,019,101**

[Math.] The 14^{th} square number that is the sum of squares of 2 consecutive numbers: 31,509,019,100^{2}+31,509,019,101^{2} = 44,560,482,149^{2}. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 5^{2}, 29^{2}, 169^{2}, 985^{2}…

Or in other words:

(31,509,019,100, 31,509,019,101, 44,560,482,149) is the 14^{th} Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

**31,650,544,836**

[Math.] Sum of the first 596 cube numbers:

1^{3}+…+596^{3} = 31,650,544,836 = (1+…+596)^{2} = 177,906^{2}.

**31,772,911,120**

[Math.] Two consecutive sums of consecutive square numbers:

31,772,911,120 = 18145^{2}+…+18240^{2} = 18241^{2}+…+18335^{2}.

**31,787,109,375**

[Math.] Its odd powers end with 31,787,109,375. Its even powers end with 18,212,890,625.

**31,787,109,376**

[Math.] All of its powers end with 81,787,109,376.

**31,863,321,009**

[Math.] Sum of the first 597 cube numbers:

1^{3}+…+597^{3 }= 31,863,321,009 = (1+…+597)^{2} = 178,503^{2}.

**xy,zwv,abc,def**

[Math.] For any *xy,zwv *= 10,000 to 99,999, there are always six 6-digit numbers *abc,edf *such that *xy,zwv* +*abc,def* is equal to one of 6 digit-rotations of 142,857 and the number *xy,zwv,abc,def* is a multiple of 142,857.

For any *xy,zwv * = 10,000 to 76,922, there are always twelve 6-digit numbers *abc,edf *such that *xy,zwv* +*abc,def* is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number *xy,zwv,abc,def* is a multiple of 76,923.