[bcc: various places] From: Jud McCranie <j.mccranie@adelphia.net>

At 07:03 PM 1/6/2007, N. J. A. Sloane wrote:

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This led me to wonder about the analogous question for primes. This must be well-studied. What's the largest prime known with property that you can repeatedly delete a digit (you get to choose which digit) and still have a prime, all the way down to the empty word?

I think this is the largest known: http://primes.utm.edu/glossary/page.php?sort=DeletablePrime

Tish pish. They're everywhere and trivial to grow. 2 23 223 1223 10223 102023 1020023 10200263 102002603 1020026303 10200226303 102002263031 1020002263031 10200022363031 102000223263031 1020000223263031 10200002232630131 102000022326301313 1020000222326301313 10200002223236301313 102000012223236301313 1020000122232363013013 10200000122232363013013 102000001222320363013013 1020000012223202363013013 10120000012223202363013013 101200000122232002363013013 1012000001222320023623013013 10120000001222320023623013013 101200000012022320023623013013 1012000000112022320023623013013 10120000001120223200236230130313 101200000011202023200236230130313 1012000000112020232002362301303813 10120000001120202320020362301303813 101200000011202023200203623013036813 1010200000011202023200203623013036813 10102000000112020213200203623013036813 101020000001120202103200203623013036813 1010200000011202002103200203623013036813 10102000000112020021032002036230130326813 101002000000112020021032002036230130326813 1010020000001012020021032002036230130326813 10100200000010120200210312002036230130326813 101002000000101202002103132002036230130326813 1010020000001012020020103132002036230130326813 10100200000010120200201031320002036230130326813 100100200000010120200201031320002036230130326813 1001002000000101202002010313200020362301303265813 10010020000001012020020103132000120362301303265813 100100200000010120200201031232000120362301303265813 1001002000000101202001201031232000120362301303265813 10010020000001012020012010312320001203623013032065813 100100020000001012020012010312320001203623013032065813 1001000200000010120200120103123200012036230138032065813 10010002000000101202001201031232000120362301380320765813 100100020000001012020012010312320001203062301380320765813 1001000200000010120200120103123200012030623013803207658163 10010002000000101202001201031232000120030623013803207658163 100100020000001012020012010312320001020030623013803207658163 1001000200000010120200120103123200010200306223013803207658163 10010002000000101202001200103123200010200306223013803207658163 100100020000001012020012001031232000102003062230138032076584163 1001000200000010120020012001031232000102003062230138032076584163 10010002000000101200200120010312320001020030622301038032076584163 100100020000001012002001200103123200010200306223201038032076584163 1001000200000010120020012001031232000102003062232010380372076584163 10010002000000101200200120010312302000102003062232010380372076584163 Which was about half a second of the following, utterly inefficient (it finds all possible (probable) primes before recursing) GP script: <<< lengthen(p, l) = local(n=listcreate(10*l+10), v=[], bot=p, cut=10^l, t, i); print(p);while(l>=0,t=(bot\cut)*cut;p+=9*t;bot-=t;for(i=0,9,listinsert(n,p+cut*i,length(n)+1));l--;cut\=10);n=listsort(n);for(i=1,length(n)-1,if(n[i+1]!=n[i]&&ispseudoprime(n[i+1]),v=concat(v,[n[i+1]])));v rlengthen(seed, len) = local(r=lengthen(seed,len), i, v=len); for(i=1,length(r),rlengthen(r[i],len+1));v rlengthen(2,1)

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