santocyber/conjecturadelegendre.php

## conjecturadelegendre.php
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Conjectura de Legendre</title>
<style>
    body {
        font-family: Arial, sans-serif;
        background-color: #f3f3f3;
        margin: 0;
        padding: 0;
        display: flex;
        justify-content: center;
        align-items: center;
        height: 100vh;
    }
    .container {
        background-color: #fff;
        border-radius: 10px;
        box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);
        padding: 20px;
        text-align: center;
    }
    h1 {
        margin-top: 0;
        color: #333;
    }
    p {
        margin: 10px 0;
        color: #666;
    }
    .highlight {
        color: #ff5733; /* Destaque em laranja */
        font-weight: bold;
    }
</style>
</head>
<body>
    <div class="container">
        <h1>Conjectura de Legendre</h1>
        <div id="legendreOutput"></div>
    </div>

    <script>
        let legendrePairs = []; // Lista para armazenar os pares de quadrados primos já calculados

        function isPrime(num) {
            if (num <= 1) return false;
            if (num <= 3) return true;
            if (num % 2 === 0 || num % 3 === 0) return false;
            for (let i = 5; i * i <= num; i += 6) {
                if (num % i === 0 || num % (i + 2) === 0) {
                    return false;
                }
            }
            return true;
        }

        function getNextPrimeSquarePair(start) {
            let n = start;
            while (true) {
                let square = n * n;
                let primeSquare = square + 1;
                if (isPrime(primeSquare)) {
                    return [n, primeSquare];
                }
                n++;
            }
        }

        function displayNextLegendrePair() {
            let [n, primeSquare] = getNextPrimeSquarePair(legendrePairs.length === 0 ? 1 : legendrePairs[legendrePairs.length - 1][0] + 1);
            legendrePairs.push([n, primeSquare]);

            let outputDiv = document.getElementById('legendreOutput');
            let square = n * n;
            let nextSquare = (n + 1) * (n + 1);

            let html = `<p>Conjectura de Legendre para ${n}:</p>`;
            html += `<p>Entre ${square} e ${nextSquare}: <span class="${isPrime(primeSquare) ? 'highlight' : ''}">${primeSquare}</span> ${isPrime(primeSquare) ? 'é primo' : 'não é primo'}</p>`;

            outputDiv.innerHTML = html;
        }

        displayNextLegendrePair(); // Exiba o primeiro par de quadrados primos ao carregar
        setInterval(displayNextLegendrePair, 1000);
    </script>
</body>
</html>
	<!DOCTYPE html>
	<html lang="en">
	<head>
	<meta charset="UTF-8">
	<meta name="viewport" content="width=device-width, initial-scale=1.0">
	<title>Conjectura de Legendre</title>
	<style>
	body {
	font-family: Arial, sans-serif;
	background-color: #f3f3f3;
	margin: 0;
	padding: 0;
	display: flex;
	justify-content: center;
	align-items: center;
	height: 100vh;
	}
	.container {
	background-color: #fff;
	border-radius: 10px;
	box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);
	padding: 20px;
	text-align: center;
	}
	h1 {
	margin-top: 0;
	color: #333;
	}
	p {
	margin: 10px 0;
	color: #666;
	}
	.highlight {
	color: #ff5733; /* Destaque em laranja */
	font-weight: bold;
	}
	</style>
	</head>
	<body>
	<div class="container">
	<h1>Conjectura de Legendre</h1>
	<div id="legendreOutput"></div>
	</div>

	<script>
	let legendrePairs = []; // Lista para armazenar os pares de quadrados primos já calculados

	function isPrime(num) {
	if (num <= 1) return false;
	if (num <= 3) return true;
	if (num % 2 === 0 \|\| num % 3 === 0) return false;
	for (let i = 5; i * i <= num; i += 6) {
	if (num % i === 0 \|\| num % (i + 2) === 0) {
	return false;
	}
	}
	return true;
	}

	function getNextPrimeSquarePair(start) {
	let n = start;
	while (true) {
	let square = n * n;
	let primeSquare = square + 1;
	if (isPrime(primeSquare)) {
	return [n, primeSquare];
	}
	n++;
	}
	}

	function displayNextLegendrePair() {
	let [n, primeSquare] = getNextPrimeSquarePair(legendrePairs.length === 0 ? 1 : legendrePairs[legendrePairs.length - 1][0] + 1);
	legendrePairs.push([n, primeSquare]);

	let outputDiv = document.getElementById('legendreOutput');
	let square = n * n;
	let nextSquare = (n + 1) * (n + 1);

	let html = `<p>Conjectura de Legendre para ${n}:</p>`;
	html += `<p>Entre ${square} e ${nextSquare}: <span class="${isPrime(primeSquare) ? 'highlight' : ''}">${primeSquare}</span> ${isPrime(primeSquare) ? 'é primo' : 'não é primo'}</p>`;

	outputDiv.innerHTML = html;
	}

	displayNextLegendrePair(); // Exiba o primeiro par de quadrados primos ao carregar
	setInterval(displayNextLegendrePair, 1000);
	</script>
	</body>
	</html>