A232657 Numbers producing at least 4 primes by proper concatenation of decrements.

100, 874, 1000, 1286, 3040, 3721, 3805, 3922, 4468, 6412, 7014, 7852, 8338

Offset: 1

Author

James G. Merickel, Nov 27 2013

Keywords

• nonn
• base
• more

Comments

The very simplest example of the type of prime concerned is 43, but 100 (see Example) is the first value to produce 4 primes. 1000 is the first to do so in the fastest way possible. Proper concatenation first excludes 73 from this list, as the stem--initial--value in concatenation is itself excluded from consideration.

8338 is the first value to produce 5 primes, with terminal values 8323, 8293, 8079, 7561 and 6519.

Examples

			100 yields four primes in this way: 100 99, 100 99 98 97, 100 99 98 97 96 95 94 93 92 91, and 100 99 98 97...62 61.  As the first value to do so properly, a(1)=100.
		

Crossrefs

Cf. A152396, A152397, A172257.

Programs

PARI

is(n)=my(t=Str(n),s=4); while(n--,t=Str(t,n); if(isprime(eval(t)) && s--==0, return(1))); 0 \\ Charles R Greathouse IV, Feb 18 2014