Concatenation of Prime strings

 

 

On Thu, Oct 15, 2009 at 6:30 AM:

Hello SeqFans,

this seq seems absent from the OEIS:

S = 2,3,5,7,11,13,17,19,22,23,25,27,29,31,32,33,35,37,41,43,47,52,53,55,57,59,61,67,71,72,73,75,77,79,83,89,97,101,103,107,109,112,...

Example: 112 is in S because 112 can be seen as the concatenation of 11 and 2 -- two "prime strings"

       109 is in S because the string 109 is... prime

See also:

A105184 Primes that can be written as concatenation of two primes in decimal representation.

A019549 Primes formed by concatenating other primes.

A129800 Prime numbers that can be written as the concatenation of two other prime numbers in exactly one way.

Best,

.

__________

 

Maximilian Hasler:

 

(...)

I submitted some more terms & (new) PARI code [prime strings with leading zero are forbidden].

 

%S A152242 (PARI) is_A152242(n)={ /* If n is even, the last digit must

be 2 and [n\10] (if nonzero) must be in this sequence. (This check is

not necessary but improves speed.) */ bittest(n,0) | return( n%10==2 &

(n<10 | is_A152242(n\10))); isprime(n) & return(1); for(i=1,#Str(n)-1,

n%10^i>10^(i-1) & isprime( n%10^i ) & is_A152242( n\10^i) & return(1)) }

 

More terms:

 

2, 3, 5, 7, 11, 13, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 43, 47, 52, 53, 55, 57, 59, 61, 67, 71, 72, 73, 75, 77, 79, 83, 89, 97, 101, 103, 107, 109, 112, 113, 115, 117, 127, 131, 132, 133, 135, 137, 139, 149, 151, 157, 163, 167, 172, 173, 175, 177, 179, 181, 191, 192, 193, 195, 197, 199, 211, 213, 217, 219, 222, 223, 225, 227, 229, 231, 232, 233, 235, 237, 239, 241, 243, 247, 251, 252, 253, 255, 257, 259, 261, 263, 267, 269, 271, 272, 273, 275, 277, 279, 281, 283, 289, 292, 293, 295, 297, 307, 311, 312, 313, 315, 317, 319, 322, 323, 325, 327, 329, 331, 332, 333, 335, 337, 341, 343, 347, 349, 352, 353, 355, 357, 359, 361, 367, 371, 372, 373, 375, 377, 379, 383, 389, 397, 401, 409, 412, 413, 415, 417, 419, 421, 431, 432, 433, 435, 437, 439, 443, 449, 457, 461, 463, 467, 472, 473, 475, 477, 479, 487, 491, 499, 503, 509, 511, 513, 517, 519, 521, 522, 523, 525, 527, 529, 531, 532, 533, 535, 537, 541, 543, 547, 552, 553, 555, 557, 559, 561, 563, 567, 569, 571, 572, 573, 575, 577, 579, 583, 587, 589, 592, 593, 595, 597, 599, 601, 607, 612, 613, 615, 617, 619, 631, 641, 643, 647, 653, 659, 661, 672, 673, 675, 677, 683, 691, 701, 709, 711, 712, 713, 715, 717, 719, 722, 723, 725, 727, 729, 731, 732, 733, 735, 737, 739, 741, 743, 747, 751, 752, 753, 755, 757, 759, 761, 767, 769, 771, 772, 773, 775, 777, 779, 783, 787, 789, 792, 793, 795, 797, 809, 811, 821, 823, 827, 829, 832, 833, 835, 837, 839, 853, 857, 859, 863, 877, 881, 883, 887, 892, 893, 895, 897, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 972, 973, 975, 977, 983, 991, 997, ...

 

 

__________

 

Many thanks, Maximilian, Zakir & Neil!

 

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