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Block #13,234

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 12:44:19 PM · Difficulty 7.7884 · 6,788,308 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5ecad1bb8cbb761a894e2adc3cc083396f1354ee4fe26d0ff8039806acae71f

View on Chainz ↗

Height

#13,234

Difficulty

7.788427

Transactions

Size

201 B

Version

Bits

07c9d65f

Nonce

471

Timestamp

7/11/2013, 12:44:19 PM

Confirmations

6,788,308

Merkle Root

10c0fb7bd323580d90db3a03ab54f6e27a64bd6b9cf4762cfd5094b7590e4c40

Transactions (1)

Coinbase10c0fb7bd32358…5094b7590e4c40

1 in → 1 out16.4600 XPM108 B

AcCQ2rWn…zqnxSgib

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.

1.598 × 10¹⁰¹(102-digit number)

15985033577255557798…62858287461658188680

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

1.598 × 10¹⁰¹(102-digit number)

15985033577255557798…62858287461658188679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.598 × 10¹⁰¹(102-digit number)

15985033577255557798…62858287461658188681

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

3.197 × 10¹⁰¹(102-digit number)

31970067154511115596…25716574923316377359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.197 × 10¹⁰¹(102-digit number)

31970067154511115596…25716574923316377361

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

6.394 × 10¹⁰¹(102-digit number)

63940134309022231192…51433149846632754719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.394 × 10¹⁰¹(102-digit number)

63940134309022231192…51433149846632754721

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

1.278 × 10¹⁰²(103-digit number)

12788026861804446238…02866299693265509439

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 13234

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 b5ecad1bb8cbb761a894e2adc3cc083396f1354ee4fe26d0ff8039806acae71f

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 #13,234 on Chainz ↗