A030469
Primes which are concatenations of three consecutive primes.
Original entry on oeis.org
5711, 111317, 171923, 313741, 414347, 8997101, 229233239, 239241251, 263269271, 307311313, 313317331, 317331337, 353359367, 359367373, 383389397, 389397401, 401409419, 409419421, 439443449, 449457461
Offset: 1
(1) 5=p(3), 7=p(4), 11=p(5) gives a(1).
(2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159
- Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
- John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
- Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
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Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n],Prime[n+1],Prime[n+2]}]],{n,11000}],PrimeQ] (* Zak Seidov, Oct 16 2009 *)
concat[{a_,b_,c_}]:=FromDigits[Flatten[IntegerDigits/@{a,b,c}]]; Select[ concat/@ Partition[ Prime[ Range[200]],3,1],PrimeQ] (* Harvey P. Dale, Sep 06 2017 *)
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for(i=1,999, isprime(p=eval(Str(prime(i),prime(i+1),prime(i+2)))) & print1(p," ")) \\ M. F. Hasler, Nov 10 2009
A086041
Primes that are concatenations of 5 consecutive primes.
Original entry on oeis.org
711131719, 4753596167, 5359616771, 6771737983, 97101103107109, 101103107109113, 149151157163167, 401409419421431, 431433439443449, 479487491499503, 487491499503509, 757761769773787, 827829839853857
Offset: 1
a(1)=711131719 because 711131719 is prime and the concatenation of 7, 11, 13, 17 and 19.
A030997
Smallest prime which is a concatenation of n consecutive primes.
Original entry on oeis.org
2, 23, 5711, 2357, 711131719, 113127131137139149, 29313741434753, 107109113127131137139149, 211223227229233239241251257, 691701709719727733739743751757, 2329313741434753596167
Offset: 1
a(5) = 711131719 is the smallest prime which is the concatenation of five consecutive primes 7, 11, 13, 17 and 19.
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for(k=1,19, for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & break); print1(p,", ")) \\ M. F. Hasler, Nov 10 2009
A099727
Concatenations of six consecutive primes forming a prime.
Original entry on oeis.org
113127131137139149, 569571577587593599, 727733739743751757, 733739743751757761, 739743751757761769, 102110311033103910491051, 105110611063106910871091, 110911171123112911511153, 118111871193120112131217, 138113991409142314271429
Offset: 1
The prime 113127131137139149 is a concatenation of the consecutive primes 113, 127, 131, 137, 139 and 149.
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select(isprime, [seq(parse(cat([seq(ithprime(i), i=n+0..n+5)][])), n=1..500)])[]; # K. D. Bajpai, Mar 24 2014
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Select[FromDigits[Flatten[IntegerDigits/@#]]&/@Partition[Prime[Range[ 300]],6,1],PrimeQ] (* Harvey P. Dale, Apr 30 2020 *)
A239789
Primes which are a concatenation of prime(k), prime(k+2) and prime(k+4) for some k.
Original entry on oeis.org
172331, 233141, 717989, 137149157, 191197211, 197211227, 223229239, 229239251, 257269277, 331347353, 353367379, 359373383, 467487499, 521541557, 617631643, 619641647, 647659673, 677691709, 733743757, 787809821, 797811823, 103310491061, 106110691091, 109711091123
Offset: 1
172331 is a prime and appears in the sequence because it is the concatenation of prime(7), prime(7+2) and prime(7+4).
233141 is a prime and appears in the sequence because it is the concatenation of prime(9), prime(9+2) and prime(9+4).
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with(StringTools): KD := proc() local a,b,d,e; a:=ithprime(n); b:=ithprime(n+2); d:=ithprime(n+4);
e:= parse(cat(a,b,d)); if isprime(e) then RETURN (e); fi; end: seq(KD(), n=1..500);
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Select[Table[FromDigits[Flatten[{IntegerDigits[Prime[n]], IntegerDigits[Prime[n+2]], IntegerDigits[Prime[n+4]]}]], {n,1,500}],PrimeQ]
A239974
Primes which are a concatenation of prime(k+4), prime(k+2) and prime(k) for some k.
Original entry on oeis.org
1373, 433729, 615343, 797161, 837367, 897971, 149137127, 193181173, 227211197, 337317311, 367353347, 401389379, 443433421, 557541521, 577569557, 587571563, 757743733, 811797773, 823811797, 10191009991, 10211013997, 116311511123, 120111871171, 130713011291
Offset: 1
1373 is a prime and appears in the sequence because it is the concatenation of prime(2+4), prime(2+2) and prime(2).
433729 is a prime and appears in the sequence because it is the concatenation of prime(10+4), prime(10+2) and prime(10).
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with(StringTools): KD := proc() local a, b, d, e; a:=ithprime(n+4); b:=ithprime(n+2); d:=ithprime(n); e:= parse(cat(a, b, d)); if isprime(e) then RETURN (e); fi; end: seq(KD(), n=1..500);
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Select[Table[FromDigits[Flatten[{IntegerDigits[Prime[n+4]],IntegerDigits[Prime[n+2]], IntegerDigits[Prime[n]]}]], {n,1,500}], PrimeQ]
Showing 1-6 of 6 results.
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