PROPOSITION 1
A number N of the form (100M+21 ) is a product (10A+1)*(10B+1) if and only if
A+B = 2(MOD10)

PROPOSITION 2
A number N of the form (100M+21) is a product (10A+9)*(10B+9) if and only if
A+B = 6(MOD10)

PROPOSITION 3
A number N of the form (100M+21) is a product (10A+3)*(10B+7) if and only if does exist numbers A,B that satisfyes

10AB+3A+7B = ((N-1)/10)-2

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THE FIRST PROP LED US TO THE FOLLOWING CONGRUENCES

M= 1(MOD11)
M=28(MOD31)
M=28(MOD91)
M=33(MOD41)
M=33(MOD81)
M=36(MOD51)
M=36(MOD71)
M=37(MOD61)

TYHE 2ND PROP LED US TO

M= 6(MOD 9)
M= 6(MOD69)
M=11(MOD19)
M=11(MOD59)
M014(MOD29)
M=14(MOD49)
M=15(MOD39)
M=78(MOD79)
M=78(MOD99)
M=79(MOD89)

The 3rd led us to the formula

10AB+3A+7B= 130
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If we replace M by 13 we found that 13 doesnt fit any of the congruences and

there are not integers A,B that satisfies the 3rd formula
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since we have probed that 1321 is not a product (10A+1)*(10B+1)
or (10A+9)*(10B+9) or (10A+3)*(10B+7) we have probed that

1321 IS PRIME