What is the ruling on past prayers if interspersing the fingers was obligatory and was not done, knowing that the view of Ibn Taymiyyah is adopted regarding non-repetition for the ignorant or for one who left a small spot untouched by water?

If a worshipper is uncertain about water not reaching between two fingers during ablution, the matter depends on the likelihood of water reaching:

1. If water is likely to have reached, even weakly: Re-performing the prayers is not obligatory, because the default is the validity of an act of worship after its completion, and certainty is not removed by doubt. 2. If it is certain that water did not reach except by separating or interdigitating: Majority of scholars: Re-performing the prayers whose ablution is certainly invalid is obligatory. Ibn Taymiyyah (a narration from Ahmad): Re-performing is not obligatory if one was ignorant of the ruling, because a ruling is only established by the ability to acquire knowledge.

Negligence and Ignorance of the Ruling:

The majority: Obligate re-performance in cases of negligence due to ignorance of the rulings of purification and prayer, because learning them is an individual obligation. Ibn Taymiyyah: Does not obligate re-performance for one ignorant of the ruling, and in this case, the ruling of a previous imitation does not extend to a new imitation.

Misunderstanding of Ibn Taymiyyah's Statement:

What has been attributed to Ibn Taymiyyah regarding "equating leaving a small area not reached by water with what is under the fingernail" is incorrect. What he said was an allowance for a minor impediment over which water passes, such as slight dirt under the fingernail, or minor blood and dough.

Conclusion:

Ibn Taymiyyah does not excuse leaving a part of the body untouched by water unless it is a minor impediment over which water passes, or if the person was ignorant of the obligation to wash this part. As for one who forgot or was unaware of water not reaching, re-performance is obligatory for them according to Ibn Taymiyyah.

In any case, if you were unaware of the legal ruling in the aforementioned matters, you are excused according to Ibn Taymiyyah, and re-performing the prayers is not obligatory for you.