Numbers 250,000,000,000s

250,000,000,000 & 250,000,500,000

[Math.]  (Sequence of numbers 49…950…0 and 50…050…0).

249,999,500,000,250,000,000,000 = (249,999,500,000+250,000,000,000)2 = 499,999,500,0002 and

25,000,500,002,500,000,000 = (250,000,500,000+250,000,000,000)2 = 500,000,500,0002 and 499,999,500,000+500,000,500,000 = 1,000,000,000,000.

 

250,500,250,000   

[Math.]    (Sequence of numbers 49…950…0 and 50…050…0).

 249,500,250,000 = (249,500+250,000)2 = 499,5002 and 250,500,250,000 = (250,500+250,000)2 = 500,5002 and 499,500+500,500 = 1,000,000.

 

[Math.]  Sum of the first 1000 cube numbers:

13+23+…+10003 = 250,500,250,000 = (1+…+1000)2 = 500,5002.  

 

251,503,253,001   

[Math.]  Sum of the first 1001 cube numbers:

13+23+…+10013 = 251,503,253,001 = (1+…+1001)2 = 501,5012.  

 

251,994,208,920

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

251,994,208,920 = 416162+…+417602 = 417612+…+419042.

 

252,097,800,623

[Math.]  The 10,000,000,000th prime number is 252,097,800,623.

 

252,509,265,009   

[Math.]   Sum of the first 1002 cube numbers:

13+23+…+10023 = 252,509,265,009 = (1+…+1002)2 = 502,5032

 

253,518,292,036   

[Math.]   Sum of the first 1003 cube numbers:

13+23+…+10033 = 253,518,292,036 = (1+…+1003)2 = 503,5062.  

 

254,530,340,100   

[Math.]    Sum of the first 1004 cube numbers:

13+23+…+10043 = 254,530,340,100 = (1+…+1004)2 = 504,5102.  

 

255,545,415,225   

[Math.]    Sum of the first 1005 cube numbers:

13+…+10053 = 255,545,415,225 = (1+…+1005)2 = 505,5152.

 

256,563,523,441   

[Math.]    Sum of the first 1006 cube numbers:

13+…+10063 = 256,563,523,441 = (1+…+1006)2 = 506,5212.

 

257,584,670,784   

[Math.]  Sum of the first 1007 cube numbers:

13+…+10073 = 257,584,670,784 = (1+…+1007)2 = 507,5282.

 

257,698,037,340   

[Math.]  Sum (in degrees) of all internal angles of a 1,431,655,765-side polygon. A regular 1,431,655,765-side polygon is constructible by using only straightedge and compass.

 

258,608,863,296   

[Math.]  Sum of the first 1008 cube numbers:

13+…+10083 = 258,608,863,296 = (1+…+1008)2 = 508,5362.

 

259,636,107,025   

[Math.]  Sum of the first 1009 cube numbers:

13+…+10093 = 259,636,107,025 = (1+…+1009)2 = 509,5452.

 

259,717,522,849   

[Math.]  The 15th square number that is the sum of squares of 2 consecutive numbers: 183,648,021,5992+183,648,021,6002 = 259,717,522,8492. 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:   

(183,648,021,599, 183,648,021,600, 259,717,522,849) is the 15th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.