The biggest issue is not the processing time (which is dependent upon many factors) but the recipe itself.

Many older pickle recipes originally relied upon much stronger vinegars than the 5% in use today so they had an extra margin of safety that no longer exists.

We need to see the recipe first.

Carol

If your recipe doesn't have at least half vinegar that is 5 % acidity to water ratio, it cannot prevent botulism. Cucumbers are low acid vegetables and need that much acid or more to destroy botulism .
You must process all foods if they are to be stored on the shelf. Otherwise nothing has been done to destroy bacteria and you will not have a true vacuum seal.

Very common to see your question and concerns here. As you now know that safety is the biggest issue. Pickles with a high vinegar ratio, and jellies with high acid are usually fairly safe even if not done 'exactly' to the letter as far as processing times. Thats because they USUALLY have enough acid, salt, and sugar to protect the foods from supporting any botulism or nasty bacteria. Suggest that you take awhile and read through te many recent threads to see more info, hooro stories and solutions. Also keep in mind that no one here wants to make anyone else sick (or even DIE) from a bad canning.
Happy reading..

the recipe for Grandma's pickles:
1 qt. vinegar
2 qts. water
1 cup pickling salt
Let mixture come to a boil. Pack cucumbers in jars. Add 1 head dill, pinch of alum (1/4tsp.), 1 pepper pod, and 1 garlic clove. Pour hot mixture over cucumbers and put on lids. Flip upside down for 5 minutes. Check for proper seal after the jars have cooled off.

That's the recipe. I hope it gives you a better insight.

It is not safe. It is outdated. First, not enough vinegar. You must have at least half vinegar that is 5% acidity. The old recipes had vinegar that were as much as 40 percent compared to what we have nowdays.
Also ALL foods must be properly processed. The old recipe used "open kettle" in which nothing was done to actually preserve the food. Processing destroys bacteria, molds, etc. It also creates a true vacuum seal, unlike just turning them upside down or just letting them seal. You have just sealed up all the air and bacteria inside those jars without processing.
Alum will make pickles softer as they sit. It doesn't help them at all unless it is a fully fermented pickle.
Nowdays we use calcium chloride, but it has been discontinuted by Ball.
Using fresh cucumbers is the best way to insure they are crisp.

As a comparison, I MUST also state here that ALL my pickles contain at LEAST an 80% vinegar of 5% strength. More so for a very delicate pickled pepper, which are canned using 100% vinegar at 5% acidity. Again, the availabilty of the basic product PICKLE CRISP has been offered by an alternate source, and is commonly known as FOOD CRADE CALCIUM CHLOIDE. Its available through Bulk Foods, as indicated in several of my posts. Why do a few insist on miseleading people when it comes to a product found extrememly useful in canning. For what is worth, I still have FIVE BOXES of Ball Pickle Crisp here, unopened. Its use is for small batches of pickles. Additinally I have 2 pound jar of the calcium chloride which I use for larger batches.

I will have to find another pickle recipe for putting up pickles. But can I use my Grandma's recipe if once I make them I store them in the refridgerator? I love the taste of them and the recipe makes a small batch. Any suggestions on a recipe for pickles?

Kosher Dill (Heinz Recipe)

4 lbs pickling cukes
14 cloves garlic, peeled & split
1/4 cup salt
2 3/4 cups distilled or apple cider vinegar 5% acidity
2 3/4 cups water
12 to 14 sprigs fresh dill weed (or 2 T. dried dill weed or dried dill seed per jar)
28 peppercorns

Wash cucumbers; remove 1/16 inch from blossom end, cut in half lengthwise. Combine garlic and next 3 ingredients; heat to boiling. Remove garlic and place 4 halves into each clean jar, then pack cucumbers, adding 2 sprigs of dill and 4 peppercorns. Pour hot vinegar solution over cucumbers to within 1/2 inch of top. Immediately adjust covers as jar manufacturer directs. Process 10 minutes in BWB. Makes 6-7 pints.
If you want hot pickles, add dried hot chilis to each jar.

So is it safe to say our grandmothers recipe is fine if we use straight vinegar? I hope this person is still active...

"So is it safe to say our grandmothers recipe is fine if we use straight vinegar? I hope this person is still active..."

Probably but there is no way to know for sure without seeing the entire recipe. If you want to post the whole recipe one of us will be happy to evaluate it for you. And it will taste quite different too if made with straight vinegar.

Dave