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Block #23,549

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 8:23:23 PM · Difficulty 7.9603 · 6,766,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

49648fafc83c9d51bf5b233fdf2adfe5c1c10d1ec2a746bab4ea17662e0a2b0d

View on Chainz ↗

Height

#23,549

Difficulty

7.960315

Transactions

Size

195 B

Version

Bits

07f5d737

Nonce

368

Timestamp

7/12/2013, 8:23:23 PM

Confirmations

6,766,391

Merkle Root

ca7601933dd8fd92d0ce3c76eca482ab1d59bff4022eaf2f41d902df7ae0f508

Transactions (1)

Coinbaseca7601933dd8fd…d902df7ae0f508

1 in → 1 out15.7600 XPM108 B

AHwE4GaR…TA2XZSEj

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.

4.313 × 10⁸⁶(87-digit number)

43138472485387133892…23769282827936122880

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

4.313 × 10⁸⁶(87-digit number)

43138472485387133892…23769282827936122879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.313 × 10⁸⁶(87-digit number)

43138472485387133892…23769282827936122881

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

8.627 × 10⁸⁶(87-digit number)

86276944970774267785…47538565655872245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.627 × 10⁸⁶(87-digit number)

86276944970774267785…47538565655872245761

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

1.725 × 10⁸⁷(88-digit number)

17255388994154853557…95077131311744491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.725 × 10⁸⁷(88-digit number)

17255388994154853557…95077131311744491521

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

3.451 × 10⁸⁷(88-digit number)

34510777988309707114…90154262623488983039

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 23549

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 49648fafc83c9d51bf5b233fdf2adfe5c1c10d1ec2a746bab4ea17662e0a2b0d

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 #23,549 on Chainz ↗