Starting with an L is the fastest addy. Here you go:
Address: 1Loan6qcTLm6V1koTWVGbYsuxX6J1hEz8S (Balance: )
PrivkeyPart: 5KdTLDoXVGa8beAiQ4xB9PjuvQ5fW8PEPfGqbvXaHFAh32YnmTp

Case sensitive is no problem for 5 characters. Here it is:
Address: 1JtiptJgw1vTteB66ocAXAQQcdgcT3yUcb (Balance: )
PrivkeyPart: 5KbWJipYHQBxLnBt9PqUXHRDVUJvbeT5hZ2MyhZMeg1QDFvzxp6

Unless I say otherwise, this giveaway is open

I got you 2 options, I like the second one much better:
Address: 1BAtMAni2931DyAhwZMUdfyqDY6wGiCNDQ (Balance: )
PrivkeyPart: 5HusmU7hxGqiAWcJZLJrZvGvoaQidfamJ6bhuCpTFyVhfVdXVeb

Address: 1BatmanboAGH7NortEu45PcnVXHnJKcyH3 (Balance: )
PrivkeyPart: 5KDVJoBqDpfnbwnHByjhzhM7iW398CmMup5fN8gkvQgWXzLkyQL

Here you go:
Address: 1SponsafYDAaoGjvuUsVupjfAXGvMQ9t8 (Balance: )
PrivkeyPart: 5JF8A7wtZJjijDpTYr2eP4KERPc85kut1r4Cqpc2fNW5q3YK99N

Address: 1LordPnEi77bqPHj93hKYS1Cic8JwrecaE (Balance: )
PrivkeyPart: 5JAn9Ei3Q1RKSGtJKvW98x5GGuB1UhTxP3ZE9dWBCHi26usBhMe

You're welcome

Go ahead

"PrivkeyPart": note the "Part". The Instructions in the OP explain how to use it.
But don't trust my word for it: Try to use any of the PrivkeyParts from this topic to access the account See what happens

It varies, usually a few days.

The only cap is how much time and computing power you have.

You can use both. But I'm not sure what the implications are, as they use the same part private key. That links them together now, I think (but I'm not 100% sure) if one would get compromised, the other one is no longer safe either.

7 characters is a bit much for a giveaway. Since I didn't need my computer for a while, I got you one anyway, just case insensitive:
Address: 1EBeSEDeyqjaQz3EAP7mQn6KWPHt1Fb4WH (Balance: )
PrivkeyPart: 5KG899d3KT68w7YvkGN4KfkeVXSmEC4FUbdSGeGWkjJeQV2z9vF

1Decode is 50 times more likely than 1decode, so I got you this one:
Address: 1DecodejtC6yUjnL7DzCeZ2Do8LoYjCi9q (Balance: )
PrivkeyPart: 5HtGgCCrNh7yemq7gBKh4c3Z8dSZC8QR25UgehPtT8HyYaDEoNh

I tried for 1decode or 1Decoded overnight, but it did not show up.

Can you share a public key as described in the topic start?

"l" is not possible. I got you these two options:
#1
Address: 1JAMALMRib5H3JSvt8Cc4BQ6oZwe45FHiF (Balance: )
PrivkeyPart: 5Jw465TnJVJ9CadHsE4BWXfiioEDFhpeKYPkoysjFPfNNWD2iv2
#2
Address: 1JAMALjpkZxhaw27EhzAeLvuiRNGBHxbgY (Balance: )
PrivkeyPart: 5HygE4hG9RyhkMaPaAwBmjkdCZRfkBaZ6v22KEPJ4J1wUNQrxjQ

Address: 125456Ai5XGtPUm3niWm55PKf3v1ipHRwe (Balance: )
PrivkeyPart: 5Kc3uWr3rohi7WEaaQAh21NiFhNhSu7Xecud6qaQvLTRSk4ZKX

Are you sure you didn't mean this one?
Address: 123456CiVHLwwGfzgGyoK44g72uXSVaghs (Balance: )
PrivkeyPart: 5J77zgxcA5VmAxwL5DBonDXbZ3B2DRuhx98uQWHWCHGAuq326DZ

7 characters is too long for this giveaway.

Address: 1TTips7Pze3MQFg39pyZJX7CsNLt4uMSZ (Balance: )
PrivkeyPart: 5KFWa7dx4VkQghKJRZxekzxZMWUJJfbtiGhxSWQdYuYHqTaFZJ9

That's up to your preference. Blockchain.info can do it, and I'm sure many more can too.

Now we're talking
Address: 1JustDgVhsDZRdXqY4nfWSGNrw4SFp7Jvf
PrivkeyPart: 5KSetJinUC6ezgBgwuuv1PrYTz3J1sRRtGkwKKfm9cogAQ7djFA

#1
Address: 1tRAdERkvpZYqKsivSektWLXVvGNQwwxz (Balance: )
PrivkeyPart: 5JTvTjLGgQyyNaUYvXcgUs7eYgcJWGXrtoy9Kgz35uMutNNzotY
#2
Address: 1tRAdER4aKLQDU9hKRgBPDMw7787ZXEPB (Balance: )
PrivkeyPart: 5JAq2w88XeqVmnCDYaYvR5pCQ88iy9eWwHH6YJTo8BAvyBkEyKj

This is case sensitive as it is 6 characters. I can't say it looks Pretty as intended though #2 has exactly the same case-distribution.

7 prefixes is too much for a giveaway, case sensitive it can take days. Case insensitive I gave it 30% chance but didn't find it.

Which step? Step 5 or 6?

1ElMoIsEvil would take many years, even case insensitive. 1waszum made me realize 6 digits is too much for a giveaway, but difficulty varies per prefix. I can make you a case insensitive 1waszum quite fast:

Address: 1wASzUMxoj8X8bgqxaWLBLmrHAsSgqhk9 (Balance: )
PrivkeyPart: 5KBitQJGstBfJGcQ2VCtHEpDhxDVBQ9YR7dfrduQxbDNMoELeVc

Don't you love having a bitcoin address that starts with a name, something pretty, or just something that suits you? You can find them yourself brute-force using vanitygen, or I can make one for you.
How about 1Pretty3icg1......?

Limitations

• All addresses start with 1 ^(one)
• Most characters are allowed, except for l ^{(lower case L)}, I ^{(upper case i)}, 0 ^(zero) and O ^{(upper case o)}. You can replace these characters by something else, 1HiDE would be possible, or 1HeLLo
• Finding an address is based on computing power, and luck. There are no guarantees
• Difficulty increases exponentially with prefix-length
• Addresses starting with upper case are (usually) much easier than lower case. 1Loyce takes the same amount of time to find as 1oyce
• A 1 ^(one) is extremely more difficult to find than any other character, so 111111 would take 50 times longer than 1Loyce
• 4 prefix characters are easy to find, 5 is okay too, but 6 (case insensitive) is the limit for this giveaway (and please don't ask for 111111, it is not possible)
• 7 prefix characters is too much for this giveaway, but I can make you an offer if you post your request.

New link
I'm closing this thread.
I've opened a new one: Pretty Addy Giveaway - part 2, feel free to request your addy there.

Instructions
I can just create an address, and send you the private key. This means you have to trust me, my computer, my cat, both our email clients, and by definition it can no longer be used for cold storage. So let's not. Instead, use split key:
Step 1: Goto https://www.bitaddress.org/ move your mouse/type in the field until it shows 100% and wait a second.
Step 1.5: Optional but highly recommended. Download the page, verify the download and run it locally.
Step 2: Click Vanity Wallet click the generate buttion next to “Generate your "Step1 Key Pair"
Step 3: Reply to this thread with your public key and the prefix for your address. Save the private key somewhere safe. You will need it later when I generated your partial private key. Also, let me know if your preferred prefix is case sensitive, or any case is okay (the latter is much faster)
Step 4: Once you received your partial private key, go back to bitaddress.org and click on Vanity Wallet.
Step 5: Go to step 2 Calculate your vanity wallet. In the first field put the private key you saved and in the second field put the partial private key I gave you. Click Add and Calculate Vanity Wallet
Step 6: Copy the Vanity Private Key (WIF) and import it into your preferred wallet. For paper wallets I like https://bitcoinpaperwallet.com/ (download and use offline).
Credits to shorena for most of these instructions!
If something doesn't work as expected, have a look at this example.

Bonus
Tag this address on blockchain.info, so it shows up on blockchain.info with only the prefix instead of the full address. I have done this for 1foreverDArUNEX2gVD26vautcx3b8zTZ (the tag only shows up once there is a transaction).

Why
Why do I do this? I like it! I've been making vanity addresses for a while, I now have more than I can ever use, so why not give them away?
I hope this will be a nice long-running giveaway, but I feel the need for a disclaimer:

Disclaimer
I offer no guarantees whatsoever, I can deny any request that would take too much computing time, and I can stop or change this giveaway at any moment.

Donations are welcome: 1foreverDArUNEX2gVD26vautcx3b8zTZ (Balance: )

I assume you mean "cell phone number", right? I would never give my phone.
If you're afraid to give your number, get a prepaid burner phone. Here I pick up a prepaid cheap Samsung phone including credit for 10 euro, and the battery lasts for weeks. This way you keep your personal number private.

Rollin Signature Campaign has 5 open slots. Note that some applicants have been denied due to low quality posts or poor English.

You could argue the same for Bitcoin! If all other altcoins would exist already, and someone would "invent" a chain with much higher fees, slower confirmations, and (almost) centralized miners now, who would buy it?