Number Theory > Prime Numbers > Prime Number Sequences v
Number Theory > Sequences v


Integer Sequence Primes

Just as many interesting integer sequences can be defined and their properties studied, it is often of interest to additionally determine which of their elements are prime. The following table summarizes the indices of the largest known prime (or probable prime) members of a number of named sequences.

sequence Sloane digits discoverer search limit comments
alternating factorial A001272 9158 32308 Lewis, Jobling, and Nash 9158 probable prime; search underway by E. W. Weisstein
Apéry number A092825 6624 10136 E. W. Weisstein (Mar. 2004) 104 (E. W. Weisstein, Mar. 2004) probable prime
Apéry number   8 7 E. W. Weisstein (Mar. 2004) 1103800 (E. W. Weisstein, Mar. 16, 2004)  
Bell number A051130 2841 6531   22553 (E. W. Weisstein, Mar. 5, 2005) proven prime by I. L. Canestro in 2004; search underway by E. W. Weisstein
Bernoulli number numerator A092132 42 22 E. W. Weisstein (Mar. 2004) 44800 (E. W. Weisstein, Mar. 5, 2005) probable prime; search underway by E. W. Weisstein
Carol number A091515 226749 136517 S. Harvey (2005)  
Catalan-Mersenne number   4 39 Catalan (1876) has no prime factor less than 1051 Noll; private correspondence with C. K. Caldwell, Aug. 10, 2003
central trinomial coefficient   4 2 J. Vos Post (Feb. 2005) 83786 (E. W. Weisstein, Mar. 5, 2005) search underway by E. W. Weisstein
central trinomial coefficient cousin A104010 31877 11139 E. W. Weisstein (Feb. 25, 2005) 105 (E. W. Weisstein, Mar. 7, 2005)  
consecutive number sequences consecutive cubes   - -   10200 (E. W. Weisstein, Mar. 5, 2005) none known; search underway by E. W. Weisstein
consecutive number sequences consecutive integers   - -   20856 (E. W. Weisstein, Mar. 5, 2005) none known; search underway by E. W. Weisstein
consecutive number sequences consecutive odd A046036 2570 9725   14604 (E. W. Weisstein, Mar. 5, 2005) probable prime; search underway by E. W. Weisstein
consecutive number sequences consecutive primes A046035 1429 5719   12942 (E. W. Weisstein, Mar. 5, 2005) probable prime; search underway by E. W. Weisstein
consecutive number sequences consecutive squares   3 3   11516 (E. W. Weisstein, Mar. 5, 2005) search underway by E. W. Weisstein
consecutive number sequences reverse integers   82 155   19413 (E. W. Weisstein, Mar. 5, 2005) probable prime; no others known; search underway by E. W. Weisstein
Cullen number A005849 481899 145072      
Delannoy number   8 6 E. W. Weisstein (Mar. 2004) 3530200 (E. W. Weisstein, Mar. 26, 2004)  
double Mersenne number   7 39   60 (G. Haworth 1983) status of 61 is unknown, search being coordinated by T. Forbes
Euler number A103234 510 1062   12884 (E. W. Weisstein, Mar. 5, 2005) proven prime; search underway by E. W. Weisstein
factorial prime A002982 34790 142891     21480-34790 incompletely searched; search underway by E. W. Weisstein
factorial prime A002981 26951 107707     search underway by E. W. Weisstein
factorial sums A100289 3175 19483 T. D. Noe (Dec. 11, 2004) 4000 (T. D. Noe) probable prime; sequence must be finite
Fermat prime   4 5   32  
Fibonacci prime A001605 590041 123311 H. Lifchitz (Jan. 2005)   probable prime
Harmonic number numerator A056903 27754 12035 E. W. Weisstein (Mar. 7, 2005) 28004 (E. W. Weisstein, Mar. 7, 2005) search underway by E. W. Weisstein
irregular prime A000928 5083 M. Oakes (2003)    
Kynea number A091513 110615 66597 P. Minovic (Feb. 19, 2004) 173000 (P. Minovic, C. Emmanuel)  
left factorial A100614 4769 15470 T. D. Noe    
Lucas number A001606 532277 111240 R. Lifchitz (Mar. 2004)   probable prime
Mersenne prime A000043 20996011 6320430 J. Findley (Jun. 2004)   proven prime; 42nd Mersenne prime apparently found on Feb. 18, 2005
Motzkin number A092831 36 15 E. W. Weisstein (Mar. 2004) 204300 (E. W. Weisstein, Mar. 26, 2004)  
palindromic prime A002385 104281 D. Heuer (2003)    
partition function P A046063 127080 392 E. W. Weisstein (Mar. 9, 2004)    
partition function Q A035359 320397 625 E. W. Weisstein    
Pell number A096650 79043 30256 T. D. Noe 80000 (T. D. Noe) probable prime
Pell-Lucas number A099088 90197 34525 T. D. Noe   probable prime
primorial prime A057704 1849 6845   9592 (Caldwell and Gallot 2002) search underway by E. W. Weisstein
primorial prime A014545 33237 169966   42507 (D. Heuer) 9592-33237 incompletely searched?; search underway by E. W. Weisstein
repunit A004023 86453 86453 L. Baxter (Oct. 26, 2000)    
Sophie Germain prime A005384 36523 P. Minovic (2005)    
subfactorial A100614 4769        
super Catalan number A092839 216 161 E. W. Weisstein (Mar. 2004) 584400 (E. W. Weisstein, Mar. 16, 2004)  
Thâbit ibn Kurrah number A002235 164987 49667      
tribonacci number A092835 96878 25639 K. Duszenko (Aug. 2003)   probable prime
Wilson prime A007540 563 3   (Crandall et al. 1997)  
Woodall number A002234 151023 45468      

 

Integer Sequence, Prime Number, Probable Prime




References

Caldwell, C. and Gallot, Y. "On the Primality of and ." Math. Comput. 71, 441-448, 2002.

Forbes, T. "MM61: A Search for a Factor of . Progress: 2 March 2004." http://www.ltkz.demon.co.uk/ar2/mm61prog.htm.

Harvey, S. http://www.geocities.com/harvey563/Carol_Kynea.txt.

Lifchitz, H. and Lifchitz, R. "PRP Top Records." http://www.primenumbers.net/prptop/prptop.php.

Sloane, N. J. A. Sequences A000043, A000928, A001605, A001606, A002234, A002235, A002981/M0908, A002982/M2321, A004023, A005849/M5401, A014545, A014547, A035359, A046036, A046063, A046284, A051130, A057704, A091513, A091515, A092132, A092825, A092831, A092835, A092839 in "The On-Line Encyclopedia of Integer Sequences." http://www.research.att.com/~njas/sequences/.