Numbers 1700-1799

A page of the Numeropedia - the Special Encyclopedia of Numbers

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1,700

[Calendar]   This year is a non-leap year, following the adoption of the current Gregorian calendar, created by Pope Gregory XIII in 1582 to reform the old Julian calendar.

[Calendar]   The last year of the 17th century.

[Phone]   The first 4 digits to be dialed for any 700/toll-call (cost-per-call) telephone number dialing within the U.S. and Canada.

1,701

[Calendar]   The first year of the 18th century.

1,708

[Math.]   A base system of multigrade equalities:

1+5+10+18+23+27 = 84 = 2+3+13+15+25+26

12+52+102+182+232+272 = 1,708 = 22+32+132+152+252+262

13+53+103+183+233+273 = 38,808 = 23+33+133+153+253+263

14+54+104+184+234+274 = 926,884 = 24+34+134+154+254+264

15+55+105+185+235+275 = 22,777,944 = 25+35+135+155+255+265. (References [20])

Multigrade equalities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

[Math.]  773 = 456,533  = (–456+533)3

774 = 35,153,041  = (–035+153–041)4

775 = 2,706,784,157  = (–002+706–784+157)5

776 = 208,422,380,089  = (208–422+380–089)6

778 = 1,235,736,291,547,681  = (1–235+736–291+547–681)8

779 = 95,151,694,449,171,437  = (–095+151–694+449–171+437)9

and

777 = 16,048,523,266,853 & 016–048+523–266+853 = 1,078 and –001+078 = 77.

1,709

[Math.]   A prime number.

1,710

[Tech.]   The highest frequency (1710 kHz) for an AM radio station, available for most commercial radios.

1,711

[Math.]   A triangular number (sum of all integers from 1 to 58): 1711 = 1+2+…+57+58.

1,715

[Math.]   1715 = 1×73×1×5.

1,721

[Math.]   A prime number.

1,723

[Math.]   A prime number.

1,728

[Measure]   The number of cubic inches (inch3) in a cubic foot (ft3).

1 m3 (cubic meter) = 35.31466672 ft3 = 61,023.7441 inch3.

(U.S. customary and international units for volume measures).

[Math.]   Product of the first composite numbers: 1728 = 4×6×8×9.

[Math.]   123 = 63+83+103 = 33+43+53+83+103.

1,729

[Math.]   The smallest number that is the sum of 2 cube numbers in 2 ways: 123+13 = 103+93, (discovered by Indian mathematician Srinivasa Ramanujan (1887-1920) in a conversation with English mathematician G. H. Hardy about his taxi number). The next smallest such number is 4,104 = 153+93 = 163+23. (Also: 1729 = 91×19).

[Math.]   The 3rd Carmichael number: 1729 = 7×13×19.

[Math.]   The smallest Carmichael number which is the product of 2 Carmichael numbers: 509,033,161 = 1729×294,409.

[Math.]   A Harshad number (or Niven number): 1729 is divisible by 19, where 1+7+2+9 = 19.

1,733

[Math.]   A prime number.

1,737

[Math.]   17372 = 3,017,169 = (30+1716–9)2.

1,738

[Math.]   6952 = 4×1738, using each of 9 digits 1-9 once.

1,752

[Calendar]   The year the Great Britain and its English colonies adopted the Gregorian calendar, created by Pope Gregory XIII in 1582 to reform the old Julian calendar. Then 11 days were added since 1700 was not a leap year. The date 3 September became 14 September.

1,758

[History]   The U.S. Mint of Philadelphia struck 1,758 silver dollars, the first ones minted in the U.S., on 15 Oct. 1794. Each coin has images of the Goddess of Liberty ringed by stars on the front and an eagle on the back.

1,760

[Measure]   The number of yards in a mile.

U.S. customary units for linear measures: 1 mile = 8 furlongs = 320 rods = 1,760 yards = 5,280 feet = 63,360 inches.

[Music]   A frequency (Hz, Hertz) of the musical note A (La):

A0 = 27.5 Hz, A1 = 55 Hz, A2 = 110 Hz, A3 = 220 Hz, A4 = 440 Hz, A5 = 880 Hz, A6 = 1760 Hz,  A7 = 3520 Hz, A8 = 7040 Hz, A9 = 14,080 Hz and A10 = 28,160 Hz.

1,764

[Math.]  A base system of multigrade equalities: (References [??])

1+6+6+11 = 24 = 2+3+9+10

12+62+62+112 = 194 = 22+32+92+102 and

13+63+63+113 = 1764 = 23+33+93+103.

Multigrade equalities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

1,770

[Math.]   A triangular number (sum of all integers from 1 to 59): 1770 = 1+2+…+58+59

[Math.]   The pair 780 and 990 is the 2nd smallest pair of triangular numbers whose sum (1770) and difference (210) are also triangular.

[Math.]   Professor Umbugio’s famous “The End of the World” formula: the number 1492n–1770n–1863n+2141n is divisible by 1946, for all values of n up to 1945, where 1492, 1770, 1863 are the year of the Discovery of the New World by Christopher Columbus, the Boston Massacre and the Gettysburg Address, respectively.  (E. Starke, Professor Umbugio’s prediction, American Mathematical Monthly, 54, January 1947.)

1,772

[Math.]   17723 = 5,564,051,648  = (55+64+05+1648)3.

1,776

[History]   Declaration of Independence was signed in Independence Hall, Philadelphia (on 4 July 1776): the United States of America was founded.

[Movie]   Name of TV show/series or movie: “1776”. (1972)

1,777

[Math.]   A prime number.

1,782

[Math.]   17822 = 3,175,524 = (3+1755+24)2.

1,783

[Math.]   A prime number.

1,785

[Math.]   A pyramidal number (sum of all squares of integers from 1 to 17): 1785 = 12+22+…+162+172.

1,787

[Math.]   A prime number.

[History]   The year the United States Constitution was written (on 19 September 1787, in Philadelphia). Delaware is the first state to ratify the U.S. Constitution, on 7 December 1787.

1,789

[Math.]   A prime number.

1,790

[Gov.]   The year of the first U.S. Census, then U.S. population was 3,929,214.

[Trivia]   The “17 Hundred 90 Inn” bills itself as Savannah, Georgia’s oldest inn, which is famously known by its haunted ghost.

[Trivia]   The number of steps in the Eiffel Tower, Paris, France.

1,794

[History]   The U.S. Mint of Philadelphia struck 1,758 silver dollars, the first ones minted in the U.S., on 15 Oct. 1794, which has images of the Goddess of Liberty ringed by stars on the front and an eagle on the back

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References [20]