REVERSAL-ADDITION PALINDROME TEST ON 600589 Reverse and Add Process: 1. Pick a number. 2. Reverse its digits and add this value to the original number. 3. If this is not a palindrome, go back to step 2 and repeat. Let's view this Reverse and Add sequence starting with 600589: 600589 + 985006 step 1: 1585595 + 5955851 step 2: 7541446 + 6441457 step 3: 13982903 + 30928931 step 4: 44911834 + 43811944 step 5: 88723778 + 87732788 step 6: 176456566 + 665654671 step 7: 842111237 + 732111248 step 8: 1574222485 + 5842224751 step 9: 7416447236 + 6327446147 step 10: 13743893383 + 38339834731 step 11: 52083728114 + 41182738025 step 12: 93266466139 + 93166466239 step 13: 186432932378 + 873239234681 step 14: 1059672167059 + 9507612769501 step 15: 10567284936560 + 06563948276501 step 16: 17131233213061 + 16031233213171 step 17: 33162466426232 + 23262466426133 step 18: 56424932852365 + 56325823942465 step 19: 112750756794830 + 038497657057211 step 20: 151248413852041 + 140258314842151 step 21: 291506728694192 + 291496827605192 step 22: 583003556299384 + 483992655300385 step 23: 1066996211599769 + 9679951126996601 step 24: 10746947338596370 + 07369583374964701 step 25: 18116530713561071 + 17016531703561181 step 26: 35133062417122252 + 25222171426033153 step 27: 60355233843155405 + 50455134833255306 step 28: 110810368676410711 + 117014676863018011 step 29: 227825045539428722 + 227824935540528722 step 30: 455649981079957444 + 444759970189946554 step 31: 900409951269903998 + 899309962159904009 step 32: 1799719913429808007 + 7008089243199179971 step 33: 8807809156628987978 + 8797898266519087088 step 34: 17605707423148075066 + 66057084132470750671 step 35: 83662791555618825737 + 73752881655519726638 step 36: 157415673211138552375 + 573255831112376514751 step 37: 730671504323515067126 + 621760515323405176037 step 38: 1352432019646920243163 + 3613420296469102342531 step 39: 4965852316116022585694 + 4965852206116132585694 step 40: 9931704522232155171388 + 8831715512322254071399 step 41: 18763420034554409242787 + 78724290445543002436781 step 42: 97487710480097411679568 + 86597611479008401778479 step 43: 184085321959105813458047 + 740854318501959123580481 step 44: 924939640461064937038528 + 825830739460164046939429 step 45: 1750770379921228983977957 + 7597793898221299730770571 step 46: 9348564278142528714748528 + 8258474178252418724658439 step 47: 17607038456394947439406967 + 76960493474949365483070671 step 48: 94567531931344312922477638 + 83677422921344313913576549 step 49: 178244954852688626836054187 + 781450638626886258459442871 step 50: 959695593479574885295497058 + 850794592588475974395596959 step 51: 1810490186068050859691094017 + 7104901969580508606810940181 step 52: 8915392155648559466502034198 + 8914302056649558465512935198 step 53: 17829694212298117932014969396 + 69396941023971189221249692871 step 54: 87226635236269307153264662267 + 76226646235170396263253662278 step 55: 163453281471439703416518324545 + 545423815614307934174182354361 step 56: 708877097085747637590700678906 + 609876007095736747580790778807 step 57: 1318753104181484385171491457713 + 3177541941715834841814013578131 step 58: 4496295045897319226985505035844 + 4485305055896229137985405926944 step 59: 8981600101793548364970910962788 + 8872690190794638453971010061898 step 60: 17854290292588186818941921024686 + 68642012914981868188529209245871 step 61: 86496303207570055007471130270557 + 75507203117470055007570230369468 step 62: 162003506325040110015041360640025 + 520046063140510011040523605300261 step 63: 682049569465550121055564965940286 600589 takes 63 iterations / steps to resolve into a 33 digit palindrome. REVERSAL-ADDITION PALINDROME RECORDS Most Delayed Palindromic Number for each digit length (Only iteration counts for which no smaller records exist are considered. My program records only the smallest number that resolves for each distinct iteration count. For example, there are 18-digit numbers that resolve in 232 iterations, higher than the 228 iteration record shown for 18-digit numbers, but they were not recorded, as a smaller [17-digit] number already holds the record for 232 iterations.) Digits Number Result 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 89 187 1,297 10,911 150,296 9,008,299 10,309,988 140,669,390 1,005,499,526 10,087,799,570 100,001,987,765 1,600,005,969,190 14,104,229,999,995 100,120,849,299,260 1,030,020,097,997,900 10,442,000,392,399,960 170,500,000,303,619,996 1,186,060,307,891,929,990 solves in 24 iterations. solves in 23 iterations. solves in 21 iterations. solves in 55 iterations. solves in 64 iterations. solves in 96 iterations. solves in 95 iterations. solves in 98 iterations. solves in 109 iterations. solves in 149 iterations. solves in 143 iterations. solves in 188 iterations. solves in 182 iterations. solves in 201 iterations. solves in 197 iterations. solves in 236 iterations. solves in 228 iterations. solves in 261 iterations - World Record! [View all records] This reverse and add program was created by Jason Doucette. Please visit my Palindromes and World Records page. You have permission to use the data from this webpage (with due credit). A link to my website is much appreciated. Thank you. (This program has been run 2,496,657 times since Saturday, March 9th, 2002.)