4500

[Math.]  Sum (in degrees) of all internal angles of a 27-side polygon.

[Military]  The typical size of a modern U.S. Army brigade is  4,500 troopers and 3+ regimens and Headquarters, commanded by a 1-star brigadier general.

[Business]  Dow-Jones Wilshire 4500 Completion Index.

4510-4519

[Math.]  4510 = 4444+55+11+0.

4511 = 4444+55+11+1

4512 = 4444+55+11+2

4513 = 4444+55+11+3

4514 = 4444+55+11+4

4515 = 4444+55+11+5

4516 = 4444+55+11+6

4517 = 4444+55+11+7

4518 = 4444+55+11+8

4519 = 4444+55+11+9.

[Math.]  4513, 4517 and 4519 are prime numbers.

4,527

[Math.]  Each ratio 31689/4527 = 7, using each of 9 digits 1-9 once. Or a classical way to arrange a 9-book set on 2 shelves to mark the book #7.

4,541

[Math.] 45412 = 20,620,681.

4,544

[Math.]  45443 = 93,824,221,184 = (938+2422+1184)3.

4,546.092

[Measure] 1 gallon = 4546.092 ml (milliliters).

British imperial units for dry and liquid measures: 1 bushel = 4 pecks = 8 gallons = 32 quarts = 64 pints = 256 gills = 1280 fluidounces = 36.368736 liters.

4552

[Math.]  45522 = 20,720,704.

4,554

[Math.]

 66×64 = 4224 66×67 = 4422 66×68 = 4488 66×69 = 4554 66×74 = 4884

 666×661 = 440,226 666×666 = 443,556 666×669 = 445,554 666×672 = 447,552 666×663 = 441,558 666×667 = 444,222 666×670 = 446,220 666×674 = 448,884 666×664 = 442,224 666×668 = 444,888 666×671 = 446,886 666×675 = 449,550

… (generalizable pattern) …

4560

[Math.]  A triangular number (sum of all integers from 1 to 95): 4560 = 1+2+…+94+95.

4567

[Math.]  The only 4-digit prime number whose digits are consecutive.

[Math.]  The prime number 23,456,789 has all of its partitions 23, 4567 and 89 being prime numbers.

4,589

[Math.] The ratio 36712/4589 = 8, using each of 9 digits 1-9 once. Or a classical way to arrange a 9-book set on 2 shelves to mark the book #8.

4,591

[Math.]  A prime number. The ratio 36728/4591 = 8, using each of 9 digits 1-9 once. Or a classical way to arrange a 9-book set on 2 shelves to mark the book #8.