In the following

 B =  2d  5h 204p = BaHaRaD
 m = 29d 12h 793p = traditional period of one lunar month
 S = 235 * m / 19 = 9,467,197.6315789... halaqim
HY = Hebrew Year of interest
iy = HY MOD 19
MT = molad of Tishrei


1. The most commonly known formula

MT = INT((235 * HY - 234) / 19) * m + B

2. Landau's Variant 1

MT = 13 * (HY - 1) - INT((12 * HY + 5) / 19) * m + B

3. Landau's Variant 2

MT = INT((235 * HY + 13) / 19) * m + 3d 7h 695p

4. The Serbian Method

This method was devised by Zeljko Filipovic of Serbia in 2004g.
It is to be hoped that Zeljko Filipovic will one day explain the 
derivation of his formula.

MT = INT(HY - C(iy)) * S + B

where C(iy) = 

C( 0) = 1.0510638
C( 1) = 0.9999999
C( 2) = 1.0297872
C( 3) = 1.0595744
C( 4) = 1.0085106
C( 5) = 1.0382978
C( 6) = 1.0680851
C( 7) = 1.0170212
C( 8) = 1.0468085
C( 9) = 0.9957446
C(10) = 1.0255319
C(11) = 1.0553191
C(12) = 1.0042553
C(13) = 1.0340425
C(14) = 1.0638297
C(15) = 1.0127659
C(16) = 1.0425531
C(17) = 1.0723404
C(18) = 1.0212765

Tests in QBASIC 4.5 show this method to correctly calculate 
the Tishrei moladot up to and including HY = 951,411,350H. 
The limit is due only to the QBASIC arithmetic precision and 
not to the method itself. 

5. Landau's Variant 1 of the Serbian Method

Rather than subtract the C(iy) constants, the method adds 
the constants defined below.

MT = INT(HY + C(iy)) * S + B

where C(iy) = 

C( 0) =   0.00301794
C( 1) =   0.05408177
C( 2) =   0.02429454
C( 3) =  -0.00549269
C( 4) =   0.04557114
C( 5) =   0.01578390
C( 6) =  -0.01400333
C( 7) =   0.03706050
C( 8) =   0.00727326
C( 9) =   0.05833709
C(10) =   0.02854986
C(11) =  -0.00123738
C(12) =   0.04982645
C(13) =   0.02003922
C(14) =  -0.00974801
C(15) =   0.04131582
C(16) =   0.01152858
C(17) =  -0.01825865
C(18) =   0.03280518

Tests in QBASIC 4.5 show this method to correctly calculate 
the Tishrei moladot up to and including HY = 951,411,350H. 
The limit is due only to the QBASIC arithmetic precision and 
not to the method itself. 

6. Landau's Variant 2 of the Serbian Method

In this variant, only HY is multiplied by S, 
and the base molad is included as part of the constants C(iy).

MT = INT(HY * S + C(iy)

where C(iy) = 

C( 0) =    86015.00000005
C( 1) =   569446.36842110
C( 2) =   287444.73684216
C( 3) =     5443.10526321
C( 4) =   488874.47368426
C( 5) =   206872.84210531
C( 6) =   -75128.78947363
C( 7) =   408302.57894742
C( 8) =   126300.94736847
C( 9) =   609732.31578952
C(10) =   327730.68421058
C(11) =    45729.05263163
C(12) =   529160.42105268
C(13) =   247158.78947373
C(14) =   -34842.84210521
C(15) =   448588.52631584
C(16) =   166586.89473689
C(17) =  -115414.73684206
C(18) =   368016.63157900

Tests in QBASIC 4.5 show this method to correctly calculate 
the Tishrei moladot up to and including HY = 951,411,350H. 
The limit is due only to the QBASIC arithmetic precision and 
not to the method itself. 

Ver 1  Paged 18 Apr 2004
Next Revised 18 Apr 2004