Widest Roman Prime Posted on February 5, 2016

One of my favorite joke Twitter accounts is @wacnt. It tweets things Wolfram|Alpha can’t answer. I’ve asked Facebook M to figure out a few of them and it did.

Here’s recent one that made me laugh:

widest prime less than 4000 when written as a Roman numeral in Times New Roman — @wacnt 2016-02-03

I asked M and it gave me answer pretty quickly, but I was skeptical. I after reading it closely, I realized it just gave me the largest prime under 4,000 (3,989). I was asking for the widest prime when written in Roman numerals in Times New Roman. I know it’s silly, but now I was curious.

Like anyone procrastinating, I decided this was now something I had to know before I could do anything else.

First I needed a list of primes under 4,000. Sure I could calculate this, but I figured this was a task for another time. After some quick googling, I plopped that into my script.

let primes : [ UInt ] = [ 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , 71 , 73 , 79 , 83 , 89 , 97 , 101 , 103 , 107 , 109 , 113 , 127 , 131 , 137 , 139 , 149 , 151 , 157 , 163 , 167 , 173 , 179 , 181 , 191 , 193 , 197 , 199 , 211 , 223 , 227 , 229 , 233 , 239 , 241 , 251 , 257 , 263 , 269 , 271 , 277 , 281 , 283 , 293 , 307 , 311 , 313 , 317 , 331 , 337 , 347 , 349 , 353 , 359 , 367 , 373 , 379 , 383 , 389 , 397 , 401 , 409 , 419 , 421 , 431 , 433 , 439 , 443 , 449 , 457 , 461 , 463 , 467 , 479 , 487 , 491 , 499 , 503 , 509 , 521 , 523 , 541 , 547 , 557 , 563 , 569 , 571 , 577 , 587 , 593 , 599 , 601 , 607 , 613 , 617 , 619 , 631 , 641 , 643 , 647 , 653 , 659 , 661 , 673 , 677 , 683 , 691 , 701 , 709 , 719 , 727 , 733 , 739 , 743 , 751 , 757 , 761 , 769 , 773 , 787 , 797 , 809 , 811 , 821 , 823 , 827 , 829 , 839 , 853 , 857 , 859 , 863 , 877 , 881 , 883 , 887 , 907 , 911 , 919 , 929 , 937 , 941 , 947 , 953 , 967 , 971 , 977 , 983 , 991 , 997 , 1009 , 1013 , 1019 , 1021 , 1031 , 1033 , 1039 , 1049 , 1051 , 1061 , 1063 , 1069 , 1087 , 1091 , 1093 , 1097 , 1103 , 1109 , 1117 , 1123 , 1129 , 1151 , 1153 , 1163 , 1171 , 1181 , 1187 , 1193 , 1201 , 1213 , 1217 , 1223 , 1229 , 1231 , 1237 , 1249 , 1259 , 1277 , 1279 , 1283 , 1289 , 1291 , 1297 , 1301 , 1303 , 1307 , 1319 , 1321 , 1327 , 1361 , 1367 , 1373 , 1381 , 1399 , 1409 , 1423 , 1427 , 1429 , 1433 , 1439 , 1447 , 1451 , 1453 , 1459 , 1471 , 1481 , 1483 , 1487 , 1489 , 1493 , 1499 , 1511 , 1523 , 1531 , 1543 , 1549 , 1553 , 1559 , 1567 , 1571 , 1579 , 1583 , 1597 , 1601 , 1607 , 1609 , 1613 , 1619 , 1621 , 1627 , 1637 , 1657 , 1663 , 1667 , 1669 , 1693 , 1697 , 1699 , 1709 , 1721 , 1723 , 1733 , 1741 , 1747 , 1753 , 1759 , 1777 , 1783 , 1787 , 1789 , 1801 , 1811 , 1823 , 1831 , 1847 , 1861 , 1867 , 1871 , 1873 , 1877 , 1879 , 1889 , 1901 , 1907 , 1913 , 1931 , 1933 , 1949 , 1951 , 1973 , 1979 , 1987 , 1993 , 1997 , 1999 , 2003 , 2011 , 2017 , 2027 , 2029 , 2039 , 2053 , 2063 , 2069 , 2081 , 2083 , 2087 , 2089 , 2099 , 2111 , 2113 , 2129 , 2131 , 2137 , 2141 , 2143 , 2153 , 2161 , 2179 , 2203 , 2207 , 2213 , 2221 , 2237 , 2239 , 2243 , 2251 , 2267 , 2269 , 2273 , 2281 , 2287 , 2293 , 2297 , 2309 , 2311 , 2333 , 2339 , 2341 , 2347 , 2351 , 2357 , 2371 , 2377 , 2381 , 2383 , 2389 , 2393 , 2399 , 2411 , 2417 , 2423 , 2437 , 2441 , 2447 , 2459 , 2467 , 2473 , 2477 , 2503 , 2521 , 2531 , 2539 , 2543 , 2549 , 2551 , 2557 , 2579 , 2591 , 2593 , 2609 , 2617 , 2621 , 2633 , 2647 , 2657 , 2659 , 2663 , 2671 , 2677 , 2683 , 2687 , 2689 , 2693 , 2699 , 2707 , 2711 , 2713 , 2719 , 2729 , 2731 , 2741 , 2749 , 2753 , 2767 , 2777 , 2789 , 2791 , 2797 , 2801 , 2803 , 2819 , 2833 , 2837 , 2843 , 2851 , 2857 , 2861 , 2879 , 2887 , 2897 , 2903 , 2909 , 2917 , 2927 , 2939 , 2953 , 2957 , 2963 , 2969 , 2971 , 2999 , 3001 , 3011 , 3019 , 3023 , 3037 , 3041 , 3049 , 3061 , 3067 , 3079 , 3083 , 3089 , 3109 , 3119 , 3121 , 3137 , 3163 , 3167 , 3169 , 3181 , 3187 , 3191 , 3203 , 3209 , 3217 , 3221 , 3229 , 3251 , 3253 , 3257 , 3259 , 3271 , 3299 , 3301 , 3307 , 3313 , 3319 , 3323 , 3329 , 3331 , 3343 , 3347 , 3359 , 3361 , 3371 , 3373 , 3389 , 3391 , 3407 , 3413 , 3433 , 3449 , 3457 , 3461 , 3463 , 3467 , 3469 , 3491 , 3499 , 3511 , 3517 , 3527 , 3529 , 3533 , 3539 , 3541 , 3547 , 3557 , 3559 , 3571 , 3581 , 3583 , 3593 , 3607 , 3613 , 3617 , 3623 , 3631 , 3637 , 3643 , 3659 , 3671 , 3673 , 3677 , 3691 , 3697 , 3701 , 3709 , 3719 , 3727 , 3733 , 3739 , 3761 , 3767 , 3769 , 3779 , 3793 , 3797 , 3803 , 3821 , 3823 , 3833 , 3847 , 3851 , 3853 , 3863 , 3877 , 3881 , 3889 , 3907 , 3911 , 3917 , 3919 , 3923 , 3929 , 3931 , 3943 ]

Next, I needed a way to convert an integer into Roman numerals. I thought NSNumberFormatter could do this for you, but it doesn’t. After some quick googling, I found a gist that did it and adapted it to an extension on UInt .

extension UInt { // Adapated from https://gist.github.com/kumo/a8e1cb1f4b7cff1548c7 var romanNumeral : String { let romanValues = [ "M" , "CM" , "D" , "CD" , "C" , "XC" , "L" , "XL" , "X" , "IX" , "V" , "IV" , "I" ] let arabicValues : [ UInt ] = [ 1000 , 900 , 500 , 400 , 100 , 90 , 50 , 40 , 10 , 9 , 5 , 4 , 1 ] var romanValue = "" var startingValue = self for ( index , romanChar ) in romanValues . enumerate () { let arabicValue = arabicValues [ index ] let div = startingValue / arabicValue if div > 0 { for _ in 0 ..< div { romanValue += romanChar } startingValue -= arabicValue * div } } return romanValue } }

Now all we have to do is loop through and find the widest as a string when converted to Roman numerals in Times New Roman. Easy!

import UIKit var widest : UInt = 0 var width : CGFloat = 0 let attributes = [ NSFontAttributeName : UIFont ( name : "Times New Roman" , size : 12 ) ! ] for prime in primes { let size = prime . romanNumeral . sizeWithAttributes ( attributes ) if size . width >= width { width = size . width widest = prime } } print ( "widest prime less than 4000 when written as a Roman numeral in Times New Roman: \( widest ) " )