In 1772, the great Swiss mathematician Leonhard Euler found something beautiful and surprising.
He discovered that the simple formula
f(x) = xยฒ + x + 41
produces prime numbers again and again.
If you put in whole numbers starting from x = 0 up to 39, every answer is a prime number.
Imagine Eulerโs excitement โ a neat little formula that keeps giving primes like magic.
But then came the disappointment.
When x = 40, the spell breaks. The result is no longer prime โ itโs a composite number. The magic doesnโt last forever.
Still, the formula is remarkable. Even for values from x = 40 to 79, it produces 33 prime numbers.
Thatโs an impressively high success rate for such a simple expression.
Mathematicians later searched for even better formulas. One powerful example is:
2xยฒ โ 199
For the first 1,000 values of x, this formula produces 598 prime numbers โ more than any other quadratic formula discovered so far.
These formulas donโt create an endless stream of primes. But they reveal something fascinating: hidden patterns inside numbers.
And sometimes, with nothing more than a pencil and a clever idea, mathematics feels almost magical.
Sebuah catatan awal tahun.
----
5 Januari (sebagian 12 Januari), sekolah mulai lagi.
Buku dibuka. Jadwal kembali padat.
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