REVERSAL-ADDITION PALINDROME TEST ON 1000007614641 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 1000007614641: 1000007614641 + 1464167000001 step 1: 2464174614642 + 2464164714642 step 2: 4928339329284 + 4829239338294 step 3: 9757578667578 + 8757668757579 step 4: 18515247425157 + 75152474251581 step 5: 93667721676738 + 83767612776639 step 6: 177435334453377 + 773354433534771 step 7: 950789767988148 + 841889767987059 step 8: 1792679535975207 + 7025795359762971 step 9: 8818474895738178 + 8718375984748188 step 10: 17536850880486366 + 66368408805863571 step 11: 83905259686349937 + 73994368695250938 step 12: 157899628381600875 + 578006183826998751 step 13: 735905812208599626 + 626995802218509537 step 14: 1362901614427109163 + 3619017244161092631 step 15: 4981918858588201794 + 4971028858588191894 step 16: 9952947717176393688 + 8863936717177492599 step 17: 18816884434353886287 + 78268835343448861881 step 18: 97085719777802748168 + 86184720877791758079 step 19: 183270440655594506247 + 742605495556044072381 step 20: 925875936211638578628 + 826875836112639578529 step 21: 1752751772324278157157 + 7517518724232771572571 step 22: 9270270496557049729728 + 8279279407556940720729 step 23: 17549549904113990450457 + 75405409931140994594571 step 24: 92954959835254985045028 + 82054058945253895945929 step 25: 175009018780508880990957 + 759099088805087810900571 step 26: 934108107585596691891528 + 825198196695585701801439 step 27: 1759306304281182393692967 + 7692963932811824036039571 step 28: 9452270237093006429732538 + 8352379246003907320722549 step 29: 17804649483096913750455087 + 78055405731969038494640871 step 30: 95860055215065952245095958 + 85959054225956051255006859 step 31: 181819109441022003500102817 + 718201005300220144901918181 step 32: 900020114741242148402020998 + 899020204841242147411020009 step 33: 1799040319582484295813041007 + 7001403185924842859130409971 step 34: 8800443505507327154943450978 + 8790543494517237055053440088 step 35: 17590987000024564209996891066 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step 79: 1859179269994505534753081446435604499972980967 + 7690892799944065346441803574355054999629719581 step 80: 9550072069938570881194885020790659499602700548 + 8450072069949560970205884911880758399602700559 step 81: 18000144139888131851400769932671417899205401107 + 70110450299871417623996700415813188893144100081 step 82: 88110594439759549475397470348484606792349501188 + 88110594329760648484307479357494595793449501188 step 83: 176221188769520197959704949705979202585799002376 + 673200997585202979507949407959791025967881122671 step 84: 849422186354723177467654357665770228553680125047 + 740521086355822077566753456764771327453681224948 step 85: 1589943272710545255034407814430541556007361349995 + 5999431637006551450344187044305525450172723499851 step 86: 7589374909717096705378594858736067006180084849846 + 6489484800816007606378584958735076907179094739857 step 87: 14078859710533104311757179817471143913359179589703 + 30798597195331934117471897175711340133501795887041 step 88: 44877456905865038429229076993182484046860975476744 + 44767457906864048428139967092292483056850965477844 step 89: 89644914812729086857369044085474967103711940954588 + 88545904911730176947458044096375868092721841944698 step 90: 178190819724459263804827088181850835196433782899286 + 682998287334691538058181880728408362954427918091871 step 91: 861189107059150801863008968910259198150861700991157 + 751199007168051891952019869800368108051950701981168 step 92: 1612388114227202693815028838710627306202812402972325 + 5232792042182026037260178388205183962027224118832161 step 93: 6845180156409228731075207226915811268230036521804486 + 6844081256300328621185196227025701378229046510815486 step 94: 13689261412709557352260403453941512646459083032619972 + 27991623038095464621514935430406225375590721416298631 step 95: 41680884450805021973775338884347738022049804448918603 + 30681984440894022083774348883357737912050805448808614 step 96: 72362868891699044057549687767705475934100609897727217 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step 119: 140422029557765840793439357703533420874403439793966676591913503 + 305319195676669397934304478024335307753934397048567755920224041 step 120: 445741225234435238727743835727868728628337836842534432512137544 + 445731215234435248638733826827868727538347727832534432522147544 step 121: 891472440468870487366477662555737456166685564675068865034285088 + 880582430568860576465586661654737555266774663784078864044274198 step 122: 1772054871037731063832064324210475011433460228459147729078559286 + 6829558709277419548220643341105740124234602383601377301784502771 step 123: 8601613580315150612052707665316215135668062612060525030863062057 + 7502603680305250602162608665315126135667072502160515130853161068 step 124: 16104217260620401214215316330631341271335135114221040161716223125 + 52132261716104012241153153317214313603361351241210402606271240161 step 125: 68236478976724413455368469647845654874696486355431442767987463286 1000007614641 takes 125 iterations / steps to resolve into a 65 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 2,542,488 times since Saturday, March 9th, 2002.)