Generally speaking, for optimal results you want your primers to have a melting temperature between 50-60°C.
If you have high melting temperatures ( >65°C) you run the risk of having secondary annealing.
P.S. There are a lot of free primer design tools available online. These take the Tm and other important parameters (GC content, hairpin formation, etc.) into consideration while helping you to design your primers.
Edit: One thing I forgot to mention, is that the Tm of your forward and reverse primers should be within 5°C of each other.
Generally speaking, for optimal results you want your primers to have a melting temperature between 50-60°C.
If you have high melting temperatures ( >65°C) you run the risk of having secondary annealing.
P.S. There are a lot of free primer design tools available online. These take the Tm and other important parameters (GC content, hairpin formation, etc.) into consideration while helping you to design your primers.
Edit: One thing I forgot to mention, is that the Tm of your forward and reverse primers should be within 5°C of each other.
also do not forget that you can only use the annealing temperature for that part of the oligo that anneals to the template in the first 2 cycles....do not include the restriction site and other added bases in the calculation of TM
As Mathis Wolter said the ideal TM of the primers must be between 50-60 C. Your TM is too high try to lower it down to at least 65-60 C, you can use temps of -5 C or + 5 C based on your Primers TM (i.e if you have a TM of 60C you can go either 55 C or 65 C).
Primer BLAST is one of the best online free tools you can use, link bellow
https://www.ncbi.nlm.nih.gov/tools/primer-blast/
Also oligo calculator a good online tool to check for TM as well as hairpin formation, 3' Complementarity and self-annealing sites, which is also very important to check.. Link below
Dear Wesam, a couple of general perspectives for primers Tm are important to know well before you start your work with them. Tm is the temperature, where 50% of primers remain anneal to their target.
I have noticed the best range for primers Tm is from 52 - 64 C, which is also in direct relation to primer length. More the length higher is the Tm.
As you already know that above 65C Tm, secondary priming artifacts increase, but along with this you need to take care that GC content of your primers must be must not be very high (65% or above), as then you certainly need high Tm, but the same time primers won't denature easily.
Best Tm difference among a primer pair is ideally +/- 2 C and in general must be less than 5 C as already mentioned above.
Primer Tm is in fact the magnesium concentration of a reaction, in higher Tm case, your PCR master mix magnesium content must support it.
Only in multiplex PCRs you can go even 68 C Tm or beyond.
Usually, at higher Tm primers, taq polymerase seems to be more active, as its optimal catalyzing temperature is 72 C, so a high Tm (not too high) may favor amplification efficiency.
As a rule no primer should be of less than 45 C in Tm and above 72 C in Ta.
In last, remember that Ta is the most critical variable considered for primer performance than the Tm, as it defines the temperature at which maximum amount of primers in your reaction are bound to their target. So along with the Tm, must focus seriously towards primer Ta to avoid bizarre consequences in the end.