Original entry on oeis.org
3, 297, 4, 7, 12, 45, 330, 391, 82, 85, 92, 121, 251, 124, 214, 129, 304, 130, 353, 131, 137, 139, 144, 160, 163, 192, 286, 340, 146, 315, 150, 151, 158, 144, 160, 163, 192, 286, 340, 144, 160, 163, 192, 286, 340, 170, 172, 144, 160, 163, 192, 286, 340, 207
Offset: 1
A104824
Primes from merging of 4 successive digits in decimal expansion of Pi.
Original entry on oeis.org
4159, 5897, 9323, 8419, 1693, 8209, 9749, 5923, 2089, 2803, 4211, 7253, 8111, 1117, 7019, 193, 8521, 6229, 1097, 6659, 8233, 7867, 1201, 9091, 5669, 4603, 4861, 3607, 4127, 631, 5881, 5209, 9209, 4091, 3643, 5903, 11, 113, 6521, 1511, 1609, 9433
Offset: 1
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With[{pi = FromDigits/@Partition[RealDigits[Pi, 10, 500][[1]], 4, 1]}, Select[pi, PrimeQ]] (* Vincenzo Librandi, Apr 21 2013 *)
A104826
Primes from merging of 6 successive digits in decimal expansion of Pi.
Original entry on oeis.org
314159, 358979, 589793, 462643, 971693, 169399, 592307, 348253, 534211, 808651, 844609, 822317, 725359, 502841, 102701, 288109, 612847, 337867, 104543, 815209, 925409, 917153, 665213, 951941
Offset: 1
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With[{len=6},FromDigits/@Select[Partition[RealDigits[Pi,10,1000][[1]], len,1],PrimeQ[FromDigits[#]]&&IntegerLength[FromDigits[#]]==len&]] (* Harvey P. Dale, Oct 23 2011 *)
A104825
Primes from merging of 5 successive digits in decimal expansion of Pi.
Original entry on oeis.org
14159, 35897, 58979, 38327, 97169, 71693, 39937, 9749, 30781, 20899, 34211, 64709, 47093, 82231, 84811, 46229, 81097, 56659, 66593, 86783, 85669, 66923, 34603, 93607, 60631, 9209, 25409, 54091, 25903, 113, 33053, 65213, 13841, 51941, 94151
Offset: 1
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With[{pi=FromDigits/@Partition[RealDigits[Pi,10,2000][[1]],5,1]}, Select[pi,PrimeQ]] (* Harvey P. Dale, Oct 18 2011 *)
A104842
Position of the first sequence of n subsequent digits of Pi which form a prime.
Original entry on oeis.org
1, 1, 8, 3, 2, 1, 4, 34, 30, 5, 15, 2, 6, 17, 36, 82, 12, 87, 26, 12, 25, 133, 35, 18, 17, 3, 41, 17, 234, 17, 167, 92, 251, 15, 9, 12, 31, 1, 57, 290, 4, 99, 98, 502, 48, 164, 198, 201, 128, 7, 363, 143, 11, 138, 196, 32, 230, 82, 292, 515, 334, 186, 176, 223, 57, 135, 35
Offset: 1
a(1)=1 since the first single-digit prime found, 3, is at first place, hence a(1)=1,
a(2)=1 since the first two-digit prime found, 31, is at first place, hence a(2)=1,
a(3)=8 since the first three-digit prime found, 653, is at 8th place, hence a(3)=8, ...
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pi = RealDigits[Pi, 10, 100][[1]]; f[n_] := Block[{k = 1}, While[ !PrimeQ[ FromDigits[ Take[pi, {k, k + n - 1}]]], k++ ]; k]; Table[ f[n], {n, 67}] (* Robert G. Wilson v, Mar 29 2005 *)
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a(n)={for(c=-1,default(realprecision)-n-2,ispseudoprime(Pi\.1^(n+c)%10^n)&return(c+2));error("Insufficient realprecision, please increase.")} \\ M. F. Hasler, Oct 23 2011
A104841
The first n-digit prime occurring in the decimal expansion of Pi, A000796.
Original entry on oeis.org
3, 31, 653, 4159, 14159, 314159, 1592653, 28841971, 795028841, 5926535897, 93238462643, 141592653589, 9265358979323, 23846264338327, 841971693993751, 8628034825342117, 89793238462643383, 348253421170679821, 3832795028841971693, 89793238462643383279
Offset: 1
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default(realprecision,2000); A104841(n)={for( c=0, default(realprecision)-n-2, Pi\.1^c%10 & ispseudoprime(p=Pi\.1^(n+c-1)%10^n) & return(p));error("Please increase default(realprecision) to calculate A104841("n").")} \\ M. F. Hasler, Oct 23 2011
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from sympy import S, isprime
pi = "3"+str(S.Pi.n(10**5))[2:] # or load data from file
def A104841_A198344(n): return next(((p, i+1) for i in range(len(pi)-n) if pi[i]!="0" and isprime(p:=int(pi[i:i+n]))), "not enough digits")
print([A104841_A198344(n)[0] for n in range(1, 21)]) # Michael S. Branicky, Dec 28 2022
A104830
Primes from merging of 10 successive digits in decimal expansion of Pi.
Original entry on oeis.org
5926535897, 4197169399, 1693993751, 7510582097, 348253421, 4825342117, 5822317253, 812848111, 2841027019, 8521105559, 8954930381, 4756482337, 2712019091, 5432664821, 3266482133, 6072602491, 5588174881, 8815209209
Offset: 1
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With[{pi = FromDigits/@Partition[RealDigits[Pi, 10, 500][[1]], 10, 1]}, Select[pi, PrimeQ]] (* Vincenzo Librandi, Apr 21 2013 *)
A104820
Primes with distinct digits appearing in partition of decimal expansion of Pi.
Original entry on oeis.org
53, 5897, 643, 1693, 5, 815209, 29, 13, 857, 2, 983, 367, 3, 9463, 2473, 7, 71, 7481, 8467, 560827, 7, 7, 409, 24953, 7, 631859, 2, 526193, 31, 8753, 17, 17, 857, 61, 89, 9721, 7, 415069, 59, 53, 31, 983, 8175463, 71, 601, 5, 9467, 7, 31, 367, 70289, 47, 19
Offset: 1
Start with decimal expansion of Pi: 3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4,6,2,6,4,3...
Part the sequence to the sections with distinct digits: s={3,1,4},{1,5,9,2,6},{5,3},{5,8,9,7},{9,3,2},{3,8,4,6,2},{6,4,3},...
Then sequence are primes from digits of s(): 53, 5897, 643, ...
A104823
Primes from merging of three successive digits in decimal expansion of Pi.
Original entry on oeis.org
653, 643, 433, 383, 419, 197, 971, 937, 751, 97, 307, 89, 421, 211, 67, 821, 823, 647, 709, 223, 317, 359, 811, 701, 19, 193, 521, 211, 229, 881, 109, 97, 659, 593, 461, 823, 233, 337, 271, 19, 821, 607, 491, 127
Offset: 1
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With[{pi = FromDigits/@Partition[RealDigits[Pi, 10, 500][[1]], 3, 1]}, Select[pi, PrimeQ]] (* Vincenzo Librandi, Apr 23 2013 *)
A104827
Primes from merging of 7 successive digits in decimal expansion of Pi allowing leading zeros.
Original entry on oeis.org
1592653, 6535897, 2643383, 5028841, 6939937, 3993751, 348253, 1170679, 8086513, 5822317, 1725359, 4930381, 2881097, 4612847, 3165271, 2712019, 1201909, 4914127, 917153, 1133053, 3841469, 1469519, 6951941, 9433057
Offset: 1
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With[{pi = FromDigits/@Partition[RealDigits[Pi, 10, 500][[1]], 7, 1]}, Select[pi, PrimeQ]] (* Vincenzo Librandi, Apr 21 2013 *)
Showing 1-10 of 24 results.
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