Home/Chain Registry/Block #69,187

Block #69,187

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 7:34:15 AM · Difficulty 8.9906 · 6,722,025 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbda8617a26226c3d39db7182a5834a02d9a091363abd499c2a83672ba200895

View on Chainz ↗

Height

#69,187

Difficulty

8.990595

Transactions

Size

198 B

Version

Bits

08fd97a8

Nonce

Timestamp

7/20/2013, 7:34:15 AM

Confirmations

6,722,025

Merkle Root

fd867f7f28115f7c8a833a624cd1734647fbdf80d9cb70de5636b07703bcf1aa

Transactions (1)

Coinbasefd867f7f28115f…36b07703bcf1aa

1 in → 1 out12.3500 XPM110 B

AMQ1QFyp…3r8FbPbA

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.

2.100 × 10⁹⁰(91-digit number)

21006964830604934341…15455116552489757780

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

2.100 × 10⁹⁰(91-digit number)

21006964830604934341…15455116552489757779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.100 × 10⁹⁰(91-digit number)

21006964830604934341…15455116552489757781

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

4.201 × 10⁹⁰(91-digit number)

42013929661209868683…30910233104979515559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.201 × 10⁹⁰(91-digit number)

42013929661209868683…30910233104979515561

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

8.402 × 10⁹⁰(91-digit number)

84027859322419737367…61820466209959031119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.402 × 10⁹⁰(91-digit number)

84027859322419737367…61820466209959031121

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

1.680 × 10⁹¹(92-digit number)

16805571864483947473…23640932419918062239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.680 × 10⁹¹(92-digit number)

16805571864483947473…23640932419918062241

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

3.361 × 10⁹¹(92-digit number)

33611143728967894947…47281864839836124479

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 69187

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 dbda8617a26226c3d39db7182a5834a02d9a091363abd499c2a83672ba200895

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 #69,187 on Chainz ↗