/**
* Calculate the first 500 prime numbers
* Shows detailed work and verification
*/
function isPrime(num) {
if (num < 2) return false;
if (num === 2) return true;
if (num % 2 === 0) return false;
// Only need to check up to square root of num
const sqrt = Math.sqrt(num);
for (let i = 3; i <= sqrt; i += 2) {
if (num % i === 0) return false;
}
return true;
}
function findFirstNPrimes(n) {
const primes = [];
let candidate = 2;
let checksPerformed = 0;
console.log(`Starting calculation of first ${n} prime numbers...\n`);
while (primes.length < n) {
if (isPrime(candidate)) {
primes.push(candidate);
// Show progress every 50 primes
if (primes.length % 50 === 0) {
console.log(`Progress: Found ${primes.length} primes (latest: ${candidate})`);
}
}
checksPerformed++;
candidate++;
}
console.log(`\nCompleted! Checked ${checksPerformed} candidates to find ${n} primes.\n`);
return primes;
}
// Calculate first 500 primes
const primes = findFirstNPrimes(500);
console.log('='.repeat(80));
console.log('THE FIRST 500 PRIME NUMBERS');
console.log('='.repeat(80));
console.log();
// Display in rows of 10 for readability
for (let i = 0; i < primes.length; i += 10) {
const row = primes.slice(i, i + 10);
const rowLabel = `${String(i + 1).padStart(3)}-${String(Math.min(i + 10, 500)).padStart(3)}:`;
const formattedRow = row.map(n => String(n).padStart(4)).join(', ');
console.log(rowLabel + ' ' + formattedRow);
}
console.log();
console.log('='.repeat(80));
console.log('STATISTICS');
console.log('='.repeat(80));
console.log(`Total primes found: ${primes.length}`);
console.log(`Smallest prime: ${primes[0]}`);
console.log(`Largest prime (500th): ${primes[primes.length - 1]}`);
console.log(`Sum of all 500 primes: ${primes.reduce((a, b) => a + b, 0).toLocaleString()}`);
console.log(`Average value: ${(primes.reduce((a, b) => a + b, 0) / primes.length).toFixed(2)}`);
console.log(`Median value: ${primes[249]} and ${primes[250]}`);
console.log();
console.log('='.repeat(80));
console.log('VERIFICATION - First 20 primes with divisibility check');
console.log('='.repeat(80));
for (let i = 0; i < 20; i++) {
const p = primes[i];
const factors = [];
// Check all potential factors
for (let j = 2; j < p; j++) {
if (p % j === 0) {
factors.push(j);
}
}
if (factors.length === 0) {
console.log(`Prime #${String(i + 1).padStart(2)}: ${String(p).padStart(3)} ✓ No divisors found (only 1 and ${p})`);
} else {
console.log(`Prime #${String(i + 1).padStart(2)}: ${String(p).padStart(3)} ✗ ERROR - divisible by: ${factors.join(', ')}`);
}
}
console.log();
console.log('='.repeat(80));
console.log('ANALYSIS BY RANGES');
console.log('='.repeat(80));
const ranges = [
{ start: 0, end: 100, label: '1-100' },
{ start: 100, end: 200, label: '101-200' },
{ start: 200, end: 300, label: '201-300' },
{ start: 300, end: 400, label: '301-400' },
{ start: 400, end: 500, label: '401-500' }
];
ranges.forEach(range => {
const primesInRange = primes.filter(p => p >= range.start && p < range.end);
console.log(`Range ${range.label.padEnd(10)}: ${String(primesInRange.length).padStart(2)} primes found`);
});
console.log();
console.log('='.repeat(80));
console.log('INTERESTING FACTS');
console.log('='.repeat(80));
// Twin primes (primes that differ by 2)
const twinPrimes = [];
for (let i = 0; i < primes.length - 1; i++) {
if (primes[i + 1] - primes[i] === 2) {
twinPrimes.push([primes[i], primes[i + 1]]);
}
}
console.log(`Twin primes found: ${twinPrimes.length} pairs`);
console.log(`Examples: ${twinPrimes.slice(0, 5).map(pair => `(${pair[0]}, ${pair[1]})`).join(', ')}`);
// Largest gap between consecutive primes
let largestGap = 0;
let gapLocation = null;
for (let i = 0; i < primes.length - 1; i++) {
const gap = primes[i + 1] - primes[i];
if (gap > largestGap) {
largestGap = gap;
gapLocation = [primes[i], primes[i + 1]];
}
}
console.log(`Largest gap: ${largestGap} (between ${gapLocation[0]} and ${gapLocation[1]})`);
console.log();
console.log('='.repeat(80));
console.log('CALCULATION COMPLETE');
console.log('='.repeat(80));
