# Only The Lonely These primes are just ‘Equally Lonely’

Just to update: Prime numbers are only divisible by 1 and themselves. They play a major role in discrete mathematics, perhaps the most elegant branch of mathematics. But they also do their work collectively in many current technologies, such as cryptography. Exact prime numbers are prime numbers that are no longer prime by switching any number. So they are basic, but at the same time “weak”. After all, any misspelling, in and to any number, makes it non-primary. He listens closely.

Take, for example, the number 294.001. Exact prime number? Yes, because any bold typo in the string below is “fatal” and renders it non-primary:

094001, 194001, 394001, 494001, 594001, 694001, 794001, 894001, 994001
204001, 214001, 224001, 234001, 244001, 254001, 264001, 274001, 284001
290001, 291001, 292001, 293001, 295001, 296001, 297001, 298001, 299001
294101, 294201, 294301, 294401, 294501, 294601, 294701, 294801, 294901
294011, 294021, 294031, 294041, 294051, 294061, 294071, 294081, 294091
294000, 294002, 294003, 294004, 294005, 294006, 294007, 294008, 294009

Are these prime numbers rare? They are certainly much rarer than the “regular” varieties. But all things considered, it’s okay. 294,001 is the smallest, followed by 505,447, 584,141, 604,171 and 971,767. And over a million there are many, many without limits in reality. By comparison: among the ordinary primes we already have 25 smaller than a hundred, and 78,498 less than a million. So it’s a little thinner, those exact numbers How about those broad ones?

You can type any number with or without leading zeros. 294001 or 0294001 or 00294001: anything is possible. At the end of 2020, it has been proven that primes also exist with this special property: no matter how many zeros you put in front of them, they remain sensitive. Punishment right? Small details: none found yet. But it is proved that there are prime numbers that you can put zeros in front of them infinitely and with which you may not write a single number wrong, or become non-prime.