@sigma-js/primes/primes.min.js

JavaScript library for efficient prime number detection and arithmetic, with customizable algorithms for large numbers.

module.exports=function(){let minNum=1;let maxNum=8388607;let sieveType="eratosthenes";let primeNums=[];const msgs={errNumericRange:"{0} must be {1} than or equal to {2}.",errNoTarget:"There are no {0} in the {1}.",errNotExist:"{0} does not exist.",errNotSpecify:"{0} is not specified.",errInvalidSpecify:"Please specify {0} for {1}."};const getMsg=(key,repArr=null)=>{const msg=msgs[key];return repArr?msg.replace(/{(\d+)}/g,((match,i)=>repArr[i]!==undefined?repArr[i]:match)):msg};const getMinNum=()=>minNum;const getMaxNum=()=>maxNum;const getSieveType=()=>sieveType;const genPrimeNums=()=>{primeNums=(sieveType==="eratosthenes"?genEratosthenesSieve():genAtkinSieve()).reduce(((result,isPrime,index)=>{if(isPrime)result.push(index+minNum);return result}),[])};const genEratosthenesSieve=()=>{const boolValues=new Array(maxNum-minNum+1).fill(true);if(minNum===1)boolValues[0]=false;for(let i=2;i*i<=maxNum;i++){for(let j=Math.max(i*i,Math.ceil(minNum/i)*i);j<=maxNum;j+=i){boolValues[j-minNum]=false}}return boolValues};const genAtkinSieve=()=>{const boolValues=new Array(maxNum-minNum+1).fill(false);boolValues[2-minNum]=boolValues[3-minNum]=true;for(let x=1;x*x<=maxNum;x++){for(let y=1;y*y<=maxNum;y++){let n=4*x*x+y*y;if(n>=minNum&&n<=maxNum&&(n%12===1||n%12===5)){boolValues[n-minNum]=!boolValues[n-minNum]}n=3*x*x+y*y;if(n>=minNum&&n<=maxNum&&n%12===7){boolValues[n-minNum]=!boolValues[n-minNum]}n=3*x*x-y*y;if(x>y&&n>=minNum&&n<=maxNum&&n%12===11){boolValues[n-minNum]=!boolValues[n-minNum]}}}for(let x=5;x*x<=maxNum;x++){if(boolValues[x-minNum]){for(let y=x*x;y<=maxNum;y+=x*x){boolValues[y-minNum]=false}}}return boolValues};const init=config=>{if(config?.minNum===0)throw new Error(getMsg("errNumericRange",["MinNum","greater",1]));if(config?.maxNum===0)throw new Error(getMsg("errNumericRange",["MaxNum","greater",1]));if(!config?.maxNum&&!config?.minNum&&!config?.sieveType)throw new Error(getMsg("errNotSpecify",["Setting value"]));if(config?.minNum){if(config.minNum<1)throw new Error(getMsg("errNumericRange",["MinNum","greater",1]));if(config.minNum>config?.maxNum||!config?.maxNum&&config.minNum>maxNum)throw new Error(getMsg("errNumericRange",["MinNum","less",maxNum]));minNum=config.minNum}if(config?.maxNum){if(config.maxNum<1)throw new Error(getMsg("errNumericRange",["MaxNum","greater",1]));if(!Number.isSafeInteger(config.maxNum))throw new Error(getMsg("errNumericRange",["MaxNum","less",Number.MAX_SAFE_INTEGER]));maxNum=config.maxNum}if(config?.sieveType){if(config.sieveType!=="eratosthenes"&&config.sieveType!=="atkin")throw new Error(getMsg("errInvalidSpecify",["sieveType","eratosthenes or atkin"]));sieveType=config.sieveType}genPrimeNums()};const isPrime=num=>{if(num<minNum)throw new Error(getMsg("errNumericRange",["Specified number","greater",minNum]));if(num>maxNum)throw new Error(getMsg("errNumericRange",["Specified number","less",maxNum]));return primeNums.includes(num)};const isCoprime=(a,b)=>{if(a<minNum||b<minNum)throw new Error(getMsg("errNumericRange",["Specified number","greater",minNum]));if(a>maxNum||b>maxNum)throw new Error(getMsg("errNumericRange",["Specified number","less",maxNum]));const gcd=(x,y)=>{while(y!==0){const temp=y;y=x%y;x=temp}return x};return gcd(a,b)===1};const getPrimes=(start=minNum,end=maxNum)=>{if(start<minNum)throw new Error(getMsg("errNumericRange",["Starting number","greater",minNum]));if(end>maxNum)throw new Error(getMsg("errNumericRange",["Ending number","less",maxNum]));if(start>end)throw new Error(getMsg("errNumericRange",["Starting number","less","ending number"]));const primesInRange=primeNums.filter((prime=>prime>=start&&prime<=end));return primesInRange};const getPrimesAverage=(start=minNum,end=maxNum,places=2)=>{if(places<0)throw new Error(getMsg("errNumericRange",["Decimal point position","greater",0]));const primesInRange=getPrimes(start,end);const average=primesInRange.length?primesInRange.reduce(((acc,prime)=>acc+prime),0)/primesInRange.length:0;return Number(average.toFixed(places))};const getPrimesCount=(start=minNum,end=maxNum)=>{const primesInRange=getPrimes(start,end);if(!primesInRange.length)throw new Error(getMsg("errNoTarget",["prime numbers","specified range"]));return primesInRange.length};const getPrimesIndex=(num,start=minNum,end=maxNum)=>{if(num<minNum)throw new Error(getMsg("errNumericRange",["Specified number","greater",minNum]));if(num>maxNum)throw new Error(getMsg("errNumericRange",["Specified number","less",maxNum]));const primesInRange=getPrimes(start,end);if(!primesInRange.length)throw new Error(getMsg("errNoTarget",["prime numbers","specified range"]));const position=primesInRange.indexOf(num);if(position===-1)throw new Error(getMsg("errNoTarget",["prime numbers","specified range"]));return position+1};const getPrimesMedian=(start=minNum,end=maxNum)=>{const primesInRange=getPrimes(start,end);const length=primesInRange.length;if(!length)return 0;if(length%2===0){const midIndex1=length/2-1;const midIndex2=length/2;return(primesInRange[midIndex1]+primesInRange[midIndex2])/2}else{const midIndex=Math.floor(length/2);return primesInRange[midIndex]}};const getPrimesSum=(start=minNum,end=maxNum)=>{const primesInRange=getPrimes(start,end);return primesInRange.length?primesInRange.reduce(((acc,prime)=>acc+prime),0):0};const getPrimesTwins=(start=minNum,end=maxNum)=>{const primesInRange=getPrimes(start,end);if(!primesInRange.length)throw new Error(getMsg("errNoTarget",["prime numbers","specified range"]));return primesInRange.reduce(((twin,num,index,arr)=>{if(index<arr.length-1&&arr[index+1]-num===2){twin.push([num,arr[index+1]])}return twin}),[])};const getFactors=num=>{if(num<minNum)throw new Error(getMsg("errNumericRange",["Specified number","greater",minNum]));if(num>maxNum)throw new Error(getMsg("errNumericRange",["Specified number","less",maxNum]));const factors=[];let divisor=2;while(num>1&&divisor<=num){if(primeNums.includes(divisor)&&num%divisor===0){factors.push(divisor);num/=divisor}else{divisor++}}return factors};const getFactorsFormula=num=>{const factors=getFactors(num);const exponents={};factors.forEach((factor=>{exponents[factor]=(exponents[factor]||0)+1}));return Object.entries(exponents).map((([factor,exponent])=>exponent===1?factor:`${factor}^${exponent}`)).join("*")};const getMultInverse=(a,m)=>{if(a<minNum||m<minNum)throw new Error(getMsg("errNumericRange",["Specified number","greater",minNum]));if(a>maxNum||m>maxNum)throw new Error(getMsg("errNumericRange",["Specified number","less",maxNum]));if(!isCoprime(a,m))throw new Error(getMsg("errNotExist",["Multiplicative inverse"]));return Array.from({length:a*m},((_,x)=>x+1)).find((x=>a*x%m===1))};const getRandomPrime=(start=minNum,end=maxNum)=>{const primesInRange=getPrimes(start,end);if(!primesInRange.length)throw new Error(getMsg("errNoTarget",["prime numbers","specified range"]));return primesInRange[Math.floor(Math.random()*primesInRange.length)]};genPrimeNums();return{getMsg:getMsg,getMinNum:getMinNum,getMaxNum:getMaxNum,getSieveType:getSieveType,init:init,isPrime:isPrime,isCoprime:isCoprime,getPrimes:getPrimes,getPrimesAverage:getPrimesAverage,getPrimesCount:getPrimesCount,getPrimesIndex:getPrimesIndex,getPrimesMedian:getPrimesMedian,getPrimesSum:getPrimesSum,getPrimesTwins:getPrimesTwins,getFactors:getFactors,getFactorsFormula:getFactorsFormula,getMultInverse:getMultInverse,getRandomPrime:getRandomPrime}}();