17 (number)

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List of numbers — Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal

seventeen

17th
(seventeenth)

septendecimal

1, 17

XVII

10001₂

122₃

101₄

32₅

25₆

21₈

15₁₂

11₁₆

H₂₀

H₃₆

17 (seventeen) is the natural number following 16 and preceding 18. It is a prime number.

In spoken English, the numbers 17 and 70 are sometimes confused because they sound similar. When carefully enunciated, they differ in which syllable is stressed: 17 /sɛvənˈtiːn/ vs 70 /ˈsɛvənti/. However, in dates such as 1789 or when contrasting numbers in the teens, such as 16, 17, 18, the stress shifts to the first syllable: 17 /ˈsɛvəntiːn/.

The number 17 has wide significance in pure mathematics, as well as in applied sciences, law, music, religion, sports, and other cultural phenomena. 17 is the sum of the first 4 prime numbers.

In mathematics

Seventeen is the 7th prime number. The next prime is nineteen, with which it forms a twin prime.

17 is the third Fermat prime, as it is of the form 2^2ⁿ + 1, specifically with n = 2.^[1] Since 17 is a Fermat prime, regular heptadecagons can be constructed with compass and unmarked ruler. This was proven by Carl Friedrich Gauss.^[2]

There are exactly 17 two-dimensional space (plane symmetry) groups. These are sometimes called wallpaper groups, as they represent the seventeen possible symmetry types that can be used for wallpaper.

Like 41, the number 17 is a prime that yields primes in the polynomial n² + n + p, for all positive n < p − 1.

Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other natural numbers with this property. The Platonists regarded this as a sign of their peculiar propriety; and Plutarch notes it when writing that the Pythagoreans "utterly abominate" 17, which "bars them off from each other and disjoins them".^[3]

17 is the minimum possible number of givens for a sudoku puzzle with a unique solution. This was long conjectured, and was proved in 2012.^[4]

There are 17 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the 3-variable Laplace equation can be solved using the separation of variables technique.

17 is the sixth Mersenne prime exponent, yielding 131071.

17 is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest n such that x³ + y² = n has two different solutions for x and y positive integers. The next such number is 65.

17 is the minimum number of vertices on a graph such that, if the edges are coloured with 3 different colours, there is bound to be a monochromatic triangle. (See Ramsey's Theorem.)

In science

The atomic number of chlorine.
The Brodmann area defining the primary visual processing area of mammalian brains.
Group 17 of the periodic table is called the halogens.
The number of elementary particles in the Standard Model of physics.^[5]

In languages

Grammar

In Catalan, 17 is the first compound number (disset). The numbers 11 (onze) through 16 (setze) have their own names.

In French, 17 is the first compound number (dix-sept). The numbers 11 (onze) through 16 (seize) have their own names.

In Italian, 17 is also the first compound number (diciassette), whereas sixteen is sedici.

Age 17

In the UK, the minimum driving age for a car or van.
In the US and Canada, it is the age at which one may purchase, rent, or reserve M-rated video games without parental consent.
Also, in some US states,^[6] and some jurisdictions around the world, 17 is the age of sexual consent.^[7]
In most US states, Canada and in the UK, the age at which one may donate blood (without parental consent).
In many countries and regions, the age at which one may obtain a driver's license.
In the US, the age at which one may watch, rent, or purchase R-rated movies without parental consent.
In the US, the age at which one can enlist in the armed forces with parental consent.
At this age one can apply for a Private Pilot Licence (however the applicant can start training under this age.)
In Greece, the voting age.
In Chile, the minimum driving age.

In culture

Music

Bands

17 Hippies, a German band
Sytten (17 in Norwegian), a Norwegian-American rapper
Seventeen (세븐틴), a South Korean boy band
Heaven 17, an English new wave band
East 17, an English boy band

Albums

17 (Motel album)
17 (Ricky Martin album)
Chicago 17, a 1984 album by Chicago
Seventeen Days, a 2005 album by 3 Doors Down
Seventeen Seconds, a 1980 album by The Cure
17 Carat, a 2015 EP by Seventeen

Songs

"17" (Sky Ferreira song)
"17" (Yourcodenameis:Milo song)
"17 Again", a song by Eurythmics
"17 år", a song by Veronica Maggio
"17 Crimes", a song by AFI
"17 Days", a song by Prince
"17", a song by Dan Bălan
"17", a song by Jethro Tull
"17", a song by Kings of Leon
"17", a song by Milburn
"17", a song by Rick James from Reflections
"17", a B-side by Shiina Ringo on the "Tsumi to Batsu" single
"17", a song by The Smashing Pumpkins from the album Adore
"17", a song by Youth Lagoon from the album The Year of Hibernation
"17 Days" a song by Prince & the Revolution B side from the 1984 When Doves Cry single
"Seventeen" (Jet song)
"Seventeen" (Ladytron song)
"Seventeen" (Winger song)
"Seventeen", a song by ¡Forward, Russia! from Give Me a Wall
"Seventeen", a song by Jimmy Eat World from Static Prevails
"Seventeen", a song by Marina & the Diamonds from the US edition of The Family Jewels
"Seventeen", a song by Mat Kearney from the iTunes edition of Young Love
"Seventeen", a song from the Repo! The Genetic Opera soundtrack
"Seventeen", the original title of the song "I Saw Her Standing There" by The Beatles
"Seventeen", a song by the Sex Pistols from Never Mind the Bollocks, Here's the Sex Pistols
"Seventeen Forever", a song by Metro Station
"At Seventeen", a song by Janis Ian
"Edge of Seventeen", a song by Stevie Nicks
"Seventeen Ain't So Sweet", a song by The Red Jumpsuit Apparatus from Don't You Fake It
"Only 17", a song by Rucka Rucka Ali
"Opus 17 (Don't You Worry 'Bout Me)", a song by Frankie Valli and the Four Seasons
"(She's) Sexy + 17", a song by Stray Cats from Rant N' Rave with the Stray Cats
"Hello, Seventeen", a song by 12012
"Section 17 (Suitcase Calling)", a song by The Polyphonic Spree
"Day Seventeen: Accident?", a song by Ayreon
"Seventeen", a song by Alessia Cara

Other

Seventeen (musical), a 1951 American musical
The ratio 18:17 was a popular approximation for the equal tempered semitone during the Renaissance

Film

Seventeen (1916), an adaptation of the novel of the same name by Booth Tarkington
Number 17 (1928), a British-German film
Number Seventeen (1932), directed by Alfred Hitchcock
Seventeen (1940), a second adaptation of the Tarkington novel
Number 17 (1949), a Swedish film
Stalag 17 (1953), directed by Billy Wilder
Try Seventeen (2002), directed by Jeffrey Porter
In 2004, Volatile Films released a feature-length film titled The Significance of Seventeen starring Cindy Taylor; one theme addressed by the film is the high incidence of the number 17 and its function as 'the most random number' as described by MIT.
In the film Three Days of the Condor, the title character played by Robert Redford works in section 17 of the CIA.
17 Again (2009), directed by Burr Steers

Anime and manga

Android 17, a character from the Dragon Ball series.
Detective Konawaka from the Paprika anime has a strong dislike for the number 17.

Games

The computer game Half-Life 2 takes place in and around City 17.
The visual novel Ever17 strongly revolves around the number 17.

Print

The title of Seventeen, a magazine.
The title of Just Seventeen, a former magazine.
The number 17 is a recurring theme in the works of novelist Steven Brust. All of his chaptered novels have either 17 chapters or two books of 17 chapters each. Multiples of 17 frequently appear in his novels set in the fantasy world of Dragaera, where the number is considered holy.
In The Illuminatus! Trilogy, the symbol for Discordianism includes a pyramid with 17 steps because 17 has "virtually no interesting geometric, arithmetic, or mystical qualities". However, for the Illuminati, 17 is tied with the "23/17 phenomenon".
In the Harry Potter universe
- 17 is the coming of age for wizards. It is equivalent to the usual coming of age at 18.
- 17 is the number of Sickles in one Galleon in the British wizards' currency

Religion

According to Leon Kass, 17 has some significant meaning (as yet not known exactly) in the book of Genesis.^[8]
According to Plutarch's Moralia, the Egyptians have a legend that the end of Osiris' life came on the seventeenth of a month, on which day it is quite evident to the eye that the period of the full moon is over. Now, because of this, the Pythagoreans call this day "the Barrier," and utterly abominate this number. For the number seventeen, coming in between the square sixteen and the oblong rectangle eighteen, which, as it happens, are the only plane figures that have their perimeters equal their areas, bars them off from each other and disjoins them, and breaks up the epogdoon by its division into unequal intervals.^[9]
In the Yasna of Zoroastrianism seventeen chapters were written by Zoroaster himself, these are the Gathas.
The number of the raka'ahs that Muslims perform during Salat on a daily basis.
The number of surat al-Isra in the Qur'an.

In sports

17 is the number of the longest winning streak in NHL history, which the Pittsburgh Penguins achieved in 1993.
Larry Ellison's victorious 2013 Americas Cup Oracle racing yacht bears the name "17".
The number 17 has been retired in Formula 1 following Jules Bianchi's fatal accident in the 2014 Japanese Grand Prix who used number 17 in his F1 career since 2014.

In other fields

Seventeen is:

Described at MIT as 'the least random number', according to the Jargon File.^[10] This is supposedly because in a study where respondents were asked to choose a random number from 1 to 20, 17 was the most common choice.
- This study has been repeated a number of times.^[11]
The number of guns in a 17-gun salute to U.S. Army, Air Force and Marine Corps Generals, and Navy and Coast Guard Admirals.
The number of flames emanating from the grenade cap-badge of the Grenadier Guards.
During the Second World War, the four-engined heavy bomber as flown by the USAAF and other Allies and known as "The Flying Fortress", was also known as the B-17.
The maximum number of strokes of a Chinese radical.
The number of syllables in a haiku (5 + 7 + 5).
In the Nordic countries the seventeenth day of the year is considered the heart and/or the back of winter.
"Highway 17" or "Route 17": See List of highways numbered 17 and List of public transport routes numbered 17.
Seventeen, also known as Lock Seventeen, an unincorporated place in Clay Township, Tuscarawas County, Ohio.
Seventeen was the former name of a yacht prior to being commissioned in the US Navy as the USS Carnelian (PY-19).

No row 17 in Alitalia planes.

In Italian culture, the number 17 is considered unlucky. When viewed as the Roman numeral, XVII, it is then changed anagrammatically to VIXI, which in the Latin language translates to "I lived", the perfect implying "My life is over." (c.f. "Vixerunt", Cicero's famous announcement of an execution.) Renault sold its "R17" model in Italy as "R177." See Cesana Pariol in the sport section about the name of curve 17.
The fear of the number 17 is called 'heptadecaphobia' or 'heptakaidekaphobia'.
Some species of cicadas have a life cycle of 17 years (i.e. they are buried in the ground for 17 years between every mating season).
The number of special significance to Yellow Pig's Day and Hampshire College Summer Studies in Mathematics.
The number to call Police in France.
Force 17, a special operations unit of the Palestinian Fatah movement.
The number of the French department Charente-Maritime
The declared percentage alcohol content (by volume) of Baileys Irish Cream - an Irish whiskey and cream based liqueur, made by Gilbeys of Ireland.
The flight number of Malaysia Airlines Flight 17 which was shot down on 17 July 2014.

References

↑ "Sloane's A019434 : Fermat primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
↑ John H. Conway and Richard K. Guy, The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygon) could be constructed with ruler and compasses."
↑ Babbitt, Frank Cole (1936). "Plutarch's Moralia". V. Loeb.
↑ McGuire, Gary. "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem" (PDF). arXiv:1201.0749 . Retrieved 26 March 2012.
↑ Glenn Elert. "The Standard Model".
↑ "Age Of Consent By State".
↑ "Age of consent for sexual intercourse".
↑ For example, the patriarch Jacob lived 17 years after his son Joseph went missing and presumed dead, and lived 17 years after their reunion in Egypt, and the lifespans of Abraham aged 175, Isaac aged 180, and Jacob aged 147 are not a coincidence. "(The sum of the factors in all three cases is 17; of what possible significance this is, I have no idea.)" Leon Kass, The beginning of wisdom: reading Genesis,(Simon and Schuster, 2003), ISBN 978-0-7432-4299-8, p. 413 n. 10 (citing Genesis 47:28), quote from p. 629 n. 18, found at Google Books. Retrieved June 17, 2009.
↑ Plutarch, Moralia (1936). Isis and Osiris (Part 3 of 5). Loeb Classical Library edition.
↑ "random numbers". catb.org/.
↑ "The Power of 17". Cosmic Variance.

Berlekamp, E. R.; Graham, R. L. (1970). "Irregularities in the distributions of finite sequences". Journal of Number Theory. 2 (2): 152–161. MR 0269605. doi:10.1016/0022-314X(70)90015-6.

External links

Wikimedia Commons has media related to 17 (number).

Look up seventeen in Wiktionary, the free dictionary.

Properties of 17
Mathematical properties of 17 at yellowpigs.net
17
is 17 the most random number at the wayback machine.

Integers

0s
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99

100s
100 101 102 103 104 105 106 107 108 109
110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129
130 131 132 133 134 135 136 137 138 139
140 141 142 143 144 145 146 147 148 149
150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169
170 171 172 173 174 175 176 177 178 179
180 181 182 183 184 185 186 187 188 189
190 191 192 193 194 195 196 197 198 199

200s
200 201 202 203 204 205 206 207 208 209
210 211 212 213 214 215 216 217 218 219
220 221 222 223 224 225 226 227 228 229
230 231 232 233 234 235 236 237 238 239
240 241 242 243 244 245 246 247 248 249
250 251 252 253 254 255 256 257 258 259
260 261 262 263 264 265 266 267 268 269
270 271 272 273 274 275 276 277 278 279
280 281 282 283 284 285 286 287 288 289
290 291 292 293 294 295 296 297 298 299

300s
300 301 302 303 304 305 306 307 308 309
310 311 312 313 314 315 316 317 318 319
320 321 322 323 324 325 326 327 328 329
330 331 332 333 334 335 336 337 338 339
340 341 342 343 344 345 346 347 348 349
350 351 352 353 354 355 356 357 358 359
360 361 362 363 364 365 366 367 368 369
370 371 372 373 374 375 376 377 378 379
380 381 382 383 384 385 386 387 388 389
390 391 392 393 394 395 396 397 398 399

400s
400 401 402 403 404 405 406 407 408 409
410 411 412 413 414 415 416 417 418 419
420 421 422 423 424 425 426 427 428 429
430 431 432 433 434 435 436 437 438 439
440 441 442 443 444 445 446 447 448 449
450 451 452 453 454 455 456 457 458 459
460 461 462 463 464 465 466 467 468 469
470 471 472 473 474 475 476 477 478 479
480 481 482 483 484 485 486 487 488 489
490 491 492 493 494 495 496 497 498 499

500s
500 501 502 503 504 505 506 507 508 509
510 511 512 513 514 515 516 517 518 519
520 521 522 523 524 525 526 527 528 529
530 531 532 533 534 535 536 537 538 539
540 541 542 543 544 545 546 547 548 549
550 551 552 553 554 555 556 557 558 559
560 561 562 563 564 565 566 567 568 569
570 571 572 573 574 575 576 577 578 579
580 581 582 583 584 585 586 587 588 589
590 591 592 593 594 595 596 597 598 599

600s
600 601 602 603 604 605 606 607 608 609
610 611 612 613 614 615 616 617 618 619
620 621 622 623 624 625 626 627 628 629
630 631 632 633 634 635 636 637 638 639
640 641 642 643 644 645 646 647 648 649
650 651 652 653 654 655 656 657 658 659
660 661 662 663 664 665 666 667 668 669
670 671 672 673 674 675 676 677 678 679
680 681 682 683 684 685 686 687 688 689
690 691 692 693 694 695 696 697 698 699

700s
700 701 702 703 704 705 706 707 708 709
710 711 712 713 714 715 716 717 718 719
720 721 722 723 724 725 726 727 728 729
730 731 732 733 734 735 736 737 738 739
740 741 742 743 744 745 746 747 748 749
750 751 752 753 754 755 756 757 758 759
760 761 762 763 764 765 766 767 768 769
770 771 772 773 774 775 776 777 778 779
780 781 782 783 784 785 786 787 788 789
790 791 792 793 794 795 796 797 798 799

800s
800 801 802 803 804 805 806 807 808 809
810 811 812 813 814 815 816 817 818 819
820 821 822 823 824 825 826 827 828 829
830 831 832 833 834 835 836 837 838 839
840 841 842 843 844 845 846 847 848 849
850 851 852 853 854 855 856 857 858 859
860 861 862 863 864 865 866 867 868 869
870 871 872 873 874 875 876 877 878 879
880 881 882 883 884 885 886 887 888 889
890 891 892 893 894 895 896 897 898 899

900s
900 901 902 903 904 905 906 907 908 909
910 911 912 913 914 915 916 917 918 919
920 921 922 923 924 925 926 927 928 929
930 931 932 933 934 935 936 937 938 939
940 941 942 943 944 945 946 947 948 949
950 951 952 953 954 955 956 957 958 959
960 961 962 963 964 965 966 967 968 969
970 971 972 973 974 975 976 977 978 979
980 981 982 983 984 985 986 987 988 989
990 991 992 993 994 995 996 997 998 999

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