Numbers 280,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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280,540

[Math.]   A pair of amicable numbers (280540, 365084).

280,995

[Math.]   Two consecutive sums of consecutive numbers: 4225+…+4290 = 4291+…+4355 = 280,995.

281,249

[Math.]   A prime number.  Its odd powers end with 281,249. Its even powers end with 000,001.

281,771

[Math.]   281,771 = 213+311+57+75+113+132.

283,200

[Game]   The highest amount (U.S.\$) that a “Jeopardy!” player can theoretically get at the end of “Double Jeopardy!” round, going to the final round: [((6×3000–200)×2)+(6×6000–(2×400))]×2×2 = 283,200.  In the earlier years, it was only: [((6×1500–100)×2)+(6×3000–(2×200))]×2×2 = 141,600.

The highest amount (U.S.\$) that a “Jeopardy!” player can theoretically win in one game day: [((6×3000–200)×2)+(6×6000–(2×400))]×2×2×2 = 566,400. In the earlier years, it was only: [((6×1500–100)×2)+(6×3000–(2×200))]×2×2×2 = 283,200.

284,270

[Math.]   217,930,248,900 = (217,930+248,900)2 = 466,8302 and

284,270,248,900 = (284270+248900)2 = 533,1702 and 466,380+533,170 = 1,000,000.

285,714

[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.

285,778

[Math.]  The 2nd known amicable/sociable number chain: 14316 → 19116 → 31704 → 47616 → 83328 → 177792 → 295488 → 629072 → 589786 → 294896 → 358336 → 418904 → 366556 → 274924 → 275444 → 243760 → 376736 → 381028 → 285778 → 152990 → 122410 → 97946 → 48976 → 45946 → 22976 → 22744 → 19916 → 17716 → 14316. (of 28 links, currently the longest, found by P. Poulet, 1918)

287,117

[Math.]   The 25,000th prime number.

287,496

[Math.]   663 = 287,496 and 28+74+96 = 198 = 66×3.

289,940

[Math.]   213,018,248,521 = (213,018+248,521)2 = 461,5392 and

289,940,248,521 = (289940+248521)2 = 538,4612 and 461,539+538,461 = 1,000,000.