Home/Chain Registry/Block #99,248

Block #99,248

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 2:39:08 PM · Difficulty 9.3796 · 6,694,802 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

f8525a793eb6d3ecbcd6f033bf57f0d0720a0d6066ba9289e0993161ae4cf717

View on Chainz ↗

Height

#99,248

Difficulty

9.379586

Transactions

Size

200 B

Version

Bits

09612c8f

Nonce

291,111

Timestamp

8/5/2013, 2:39:08 PM

Confirmations

6,694,802

Merkle Root

987595512946bfaa9901f21e6df387de336799c6cded81305caef33b30e77e52

Transactions (1)

Coinbase987595512946bf…aef33b30e77e52

1 in → 1 out11.3500 XPM109 B

ALJ24E54…CM192Nmg

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.116 × 10⁹⁸(99-digit number)

11166757701001225108…97752310066322299540

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

1.116 × 10⁹⁸(99-digit number)

11166757701001225108…97752310066322299539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.116 × 10⁹⁸(99-digit number)

11166757701001225108…97752310066322299541

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.233 × 10⁹⁸(99-digit number)

22333515402002450217…95504620132644599079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.233 × 10⁹⁸(99-digit number)

22333515402002450217…95504620132644599081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.466 × 10⁹⁸(99-digit number)

44667030804004900434…91009240265289198159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.466 × 10⁹⁸(99-digit number)

44667030804004900434…91009240265289198161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

8.933 × 10⁹⁸(99-digit number)

89334061608009800869…82018480530578396319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.933 × 10⁹⁸(99-digit number)

89334061608009800869…82018480530578396321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.786 × 10⁹⁹(100-digit number)

17866812321601960173…64036961061156792639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 99248

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock f8525a793eb6d3ecbcd6f033bf57f0d0720a0d6066ba9289e0993161ae4cf717

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #99,248 on Chainz ↗