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About the irregular primes p with 2<p<2000

Using PARI/gp  , I find 121 irregular  primes
p such that  2< p <  2000.

In AN APPLICATION OF HIGH-SPEED COMPUTING TO FERMAT’S LAST THEOREM,
P.N.A.S., Jan. 1954, D.H. Lehmer, E. Lehmer and H. Vandiver
found using a computer 118 irregular primes between 2 and 2000.
The authors also proved Fermat’s Last Theorem for the primes
less than 2000, although this could depend on their having
tested all irregular primes less than 2000.

The discrepancy between our counts of irregular primes
below 2000 is explained by this difference:  1381, 1597
and 1877 are not listed in their table related to
irregular primes, however my computations using
PARI/gp imply that they are irregular, as follows:

1381 divides the numerator of B_{266}.
1597 divides the numerator of B_{842}.
1877 divides the numerator of B_{1026}.

Above, the notation is such that B_3, B_5, B_7
and so on are zero.

l     2a
—————–
1381 266
1597 842
1877 1026

===================================
15.

llv54:  14 ??

1279 518
1283 510
1291 206
1291 824 *
1297 202
1297 220 *
1301 176
1307 382
1307 852 *
1319 304
1327 466
1367 234
1381 266  +++
1409 358
1429 996
1439 574
1483 224
1499 94

=======================================
12.

LLV54:  11  ?

1523 1310
1559 862
1597 842   +++
1609 1356
1613 172
1619 560
1621 980
1637 718
1663 270
1663 1508 *
1669 388
1669 1086 *
1721 30
1733 810
1733 942  *

===========================================
26- 7 =  19.

LLV54:  18  ??

1753 712
1759 1520   
1777 1192
1787 1606
1789 848
1789 1442 *
1811 550
1811 698  *
1811 1520 *
1831 1274
1847 954  
1847 1016  *
1847 1558  *
1871 1794
1877 1026  +++
1879 1260
1889 242   
1901 1722
1933 1058  
1933 1320  *
1951 1656  
1979 148  
1987 510  
1993 912  
1997 772  
1997 1888  *

===========================

my count = LLV count + 3.

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Written by meditationatae

May 11, 2013 at 10:30 pm

Posted in History

Tagged with ,

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