Highest Prime is also a twin prime... NOT

[hydeer]

By coincidence, the largest known prime is also a twin prime, that is 2 larger.

[ATH]

No, it is not a twin prime. 2^77232917+1 is divisible by 3, and 2^77232917-3 is not prime:

2^77232917-3 is not prime. RES64: 6F0CC152285F2E9F. Wg8: F9C5D09F,00000000

You are welcome to run a double check of 2^77232917-3 or search for a factor of it above 1.22*10¹³. The worktodo.txt for Prime95/mprime is:
PRP=1,2,77232917,-3

It will take 2-14 days depending on your CPU speed.

[LaurV]

Originally Posted by ATH

No, it is not a twin prime. <snip> The worktodo.txt for Prime95/mprime is:
PRP=1,2,77232917,-3
It will take 2-14 days depending on your CPU speed.

[kruoli]

Is there a place to report on such values?

UID: manoli94/Oliver-PC, 2^77232917-3 completed P-1, B1=5000000, B2=500000000, E=12, Wg4: D0001B57

By the way... Title of this thread and first post don't really match. (I guess everyone saw that already, I might be a bit slow on that)

[hydeer]

One less than a primorial is always prime number. One more than a primorial may be a twin prime. For example, primorial [5] -1= 2 . 3 . 5 = 29 and primorial [5] + 1 = 31. So primorial [ 5 ] has a so called twin two years older.

[science_man_88]

Originally Posted by hydeer

One less than a primorial is always prime number

No it is not 2*3*5*7=210; 209=11*19

[Dubslow]

2*3*5*7*11*13*17 - 1 = 61 * 8369

[retina]

Originally Posted by hydeer

One less than a primorial is always prime number.

Is this a new definition of "prime number" that we were previously unaware of?

A prime number is any number that is one less than a primorial.

Seems legit to me.

[Dr Sardonicus]

I ran a simple-minded Pari script to check whether p# +/- 1 was a pseudoprime for primes p up to 500. After the prime p, a - sign appears if p# -1 is a pseudoprime; a + sign appears if p# + 1 is a pseudoprime. If neither p# - 1 nor p# + 1 is a pseudoprime, the word "neither" appears after p.

[2 +, 3 - +, 5 - +, 7 +, 11 - +, 13 - , 17 neither, 19 neither, 23 neither, 29 neither, 31 +, 37 neither, 41 - , 43 neither, 47 neither, 53 neither, 59 neither, 61 neither, 67 neither, 71 neither, 73 neither, 79 neither, 83 neither, 89 - , 97 neither, 101 neither, 103 neither, 107 neither, 109 neither, 113 neither, 127 neither, 131 neither, 137 neither, 139 neither, 149 neither, 151 neither, 157 neither, 163 neither, 167 neither, 173 neither, 179 neither, 181 neither, 191 neither, 193 neither, 197 neither, 199 neither, 211 neither, 223 neither, 227 neither, 229 neither, 233 neither, 239 neither, 241 neither, 251 neither, 257 neither, 263 neither, 269 neither, 271 neither, 277 neither, 281 neither, 283 neither, 293 neither, 307 neither, 311 neither, 313 neither, 317 - , 331 neither, 337 - , 347 neither, 349 neither, 353 neither, 359 neither, 367 neither, 373 neither, 379 +, 383 neither, 389 neither, 397 neither, 401 neither, 409 neither, 419 neither, 421 neither, 431 neither, 433 neither, 439 neither, 443 neither, 449 neither, 457 neither, 461 neither, 463 neither, 467 neither, 479 neither, 487 neither, 491 neither, 499 neither]

[rudy235]

Originally Posted by retina

Is this a new definition of "prime number" that we were previously unaware of?Seems legit to me.

Nope! It's just a new definition of the word "always".

Literally, it means "sometimes but not often"