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Search for questions, people, and topics Sign In Is the Collatz Conjecture solvable? David Cole, Formulated a mathematical model for primes based on the Goldbach Conjecture. Updated April 23, 2018 “Great thinkers have always encountered opposition from mediocre minds.” – Albert Einstein .[1] Yes!! The Collatz Conjecture is quite interesting and solvable! Here’s why: Consider the following proof of the Collatz Conjecture: Probability (Collatz sequence does not converge to one) is ∴ Probability (Collatz sequence does not converge to one) is zero. Notes: We conclude the Collatz Conjecture is true. An Important Note: The value, l_m =1, which implies division by two in the Collatz process will occur as often as all other values, l_m > 1, which imply division either by four or by eight or by sixteen or by thirty-two, … in the Collatz process according to the our probability calculations and according to the Law of Large Numbers. Thus, we expect the division by two will occur 50% of all possible divisions in the Collatz processing. That fact explains any growth in the Collatz sequence, and it also explains why the Collatz sequence will always converge to one. A Proof of Collatz Conjecture link: Proof of Collatz Conjecture . Reference links: The 3x+ 1 Problem: An Overview A Case Study of the Collatz Conjecture ; . ***** Mathematica 11 software function, f[], for simulation of data: f[m_] := ( n = m; Print[n]; prob = 1.; While[n > 1, n = 3*n + 1; Search for questions, people, and topics x = n; i = 0;cnt = 0; icnt = 0; While[ EvenQ[x], ++i; x = x/2]; s = 1 - 2^(-i); cnt = cnt + 1; If[i == 1, icnt = icnt + 1]; Print[x]; prob = prob * s; n = x; ]; Return[{m, prob, cnt, icnt, 100. * icnt/cnt}] ); Example 1: f[n_0 = 1367] yielded a probability (prob) equal to 0.0245548 before the Collatz sequence of odd integers, {1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1}, converged to one; Example 2: {n_0 =1917424378915227003508542412844973284190406292736261788098013, prob = 2.14803*10^-104, cnt = number of generated odd integers of Collatz Sequence =541, icnt =number of times l_m or i equals one = 269, icnt/cnt = 49.7227%}; Example 3: {n_0 =1134322358892035783221922112828664036984286481192427929865901, prob =1.30642*10^-113, cnt = number of generated odd integers of Collatz Sequence =573, icnt =number of times l_m or i equals one = 301, icnt/cnt = 52.5305%}; Example 4: {n_0=21346294170249129484267610567431365440581190958189557170758121139151 5390715789799022068952861978573601713877607708447514178586071267992312618 3263337224705889777568364923077634920833936889569371693845, prob =5.118883814495941*10^-344, cnt = number of generated odd integers of Collatz Sequence =1772, icnt =number of times l_m or i equals one = 902, icnt/cnt = 50.9029%}; Sign In Example 5: Search for questions, people, and topics {n_0=51270986306354174415767650068782014060235196685228248206814417094197 7788499359079526589961009312870519037650111780867282244255976210916215479 5813451432257192935153820430354322926445793164263260432795930904729611785 2464116451552006938140911375159712208272450936235369012665425381688232977 3787019813374226655258178640629301324445245691260252991300274897690542572 1961168895250648529391265350671566297565983934897155998449353970226052506 7982336871166695243225954098260027371684782477986212512395537896476946053 4655183176990277138747565943503637469154282367557173000697411352547275127 041561294264392881037, prob =8.737445781552508*10^-906, cnt = number of generated odd integers of Collatz Sequence =4745, icnt =number of times l_m or i equals one = 2361, icnt/cnt =49.7576%}; Example 6: {140632776245125940579955061295420304224335564241653342042062534292543873 7204009156598316161837868033625097692997755411598865674240723653780467274 2504346557624282178821627315905442498139231323753952791100356240353660616 7626428101307928207420696623679972454189249680086839622880004422237067288 4114602539221451613965103942130078956037214634287307961934299935536703891 3444753295595082337346237317709513828325820988051111078494941251932744193 8858817001391990343275265724180159458037564382639327656685339519800776029 3356748181656017016385303434104768138669551398789451716214418038797358811 0498638039833406945078504748652525286081427305638501766334256736229375871 2355626888648865202554555045680130195591369398482494392675971941001259654 0951482501379536530986079617422073273365156478090003328931030996278566164 9075722639143074471812229471550176979175887894029081602985328973329913929 5871255768953024559747256965074435156949271412645400791450797572891816928 8923125810989061421286135075678423238809998514907360173268373912957648911 5827533586287256506422857231047361445287462657152888404904343879264315791 3120742327499451018554718382329532651014310583830233379165659212295989150 8462805284371086426129284308767222694321354597000202120938472169382526057 2727761569575125985914732952270346475261791580440807960628067000989493125 9208386988495054075645003031988594512104837377478964596505764616218109599 6854818696682703958625899119711101464705241846416167522570556484503124967 3700776231104043246339586899159060915793189246120422686194171449795682621 2252097740262801701769222808488386035039737777825916626059163021079774776 8012170076245010675903837921982931739327741566841539391464929784221781874 1199000229948429647749192964098635391191333310149840008178019189763384818 9769673274175747209368920982080385759110035263620843502874773864652061909 7226811087286229491638080275284778648502397587582796143043321959511749393 6908404122634282699383907516940648663656336210503231496938770261232735159 529795490355396958247378256473, prob =7.060409409804900*10^-3120, cnt = number of generated odd integers of Collatz Sequence =16257, icnt =number of times l_m or i equals one = 8155, icnt/cnt =50.163%}. We expected icnt/cnt to be 50% according to the Law of Large Numbers when l_m = 1. The six examples are typical empirical affirmations of the theory proving the Collatz Conjecture. P.S. There are no exceptions (counterexamples or cycles) that disprove the Collatz Conjectue. And I challenge anyone to find one. Otherwise, it is an act of pure fiction to suggest such things without proof. Sign In Search for questions, people, and topics Sign In Footnotes [1] David Cole's answer to Are experts always right? 2.9k views · View 3 Upvoters View 5 Other Answers to this Question About the Author David Cole "What is done is finished. And what is finished is done!" Independent Research Scientist at ResearchGate.net Studied Mathematics (college major) & French (college minor) Lives in Detroit, MI 97.5k content views 2k this month More Answers from David Cole View More Is it possible that the laws of physics are not constant throughout the universe? 54 Views What is it that gives you a sense of belonging? A sense of purpose, something that gives meaning to your life? 51 Views What three laws govern the general behaviour of prime numbers? 881 Views What is the total number of integer solution that satisfies 2x+1.6y=60? 176 Views Will Professor Joseph Francisco win the Nobel Prize in Chemistry for his work on Atmospheric Chemistry? 297 Views About · Careers · Privacy · Terms · Contact