Home/Chain Registry/Block #256,794

Block #256,794

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 2:18:21 AM · Difficulty 9.9752 · 6,534,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c42d29a2dbded92d06c42bb5e957f31310dfafc6379a8ca8e6fe8df6bbbbe58f

View on Chainz ↗

Height

#256,794

Difficulty

9.975208

Transactions

Size

206 B

Version

Bits

09f9a736

Nonce

309,561

Timestamp

11/12/2013, 2:18:21 AM

Confirmations

6,534,476

Merkle Root

989996f91857c824ae9e74dea2556ecb3d083552204c62f744ba3ad9dccf64bc

Transactions (1)

Coinbase989996f91857c8…ba3ad9dccf64bc

1 in → 1 out10.0300 XPM116 B

AcLBm5Z9…S683d7c3

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.

4.689 × 10⁹³(94-digit number)

46894409183815721111…92215232275075819520

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

4.689 × 10⁹³(94-digit number)

46894409183815721111…92215232275075819519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.689 × 10⁹³(94-digit number)

46894409183815721111…92215232275075819521

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

9.378 × 10⁹³(94-digit number)

93788818367631442222…84430464550151639039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.378 × 10⁹³(94-digit number)

93788818367631442222…84430464550151639041

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

1.875 × 10⁹⁴(95-digit number)

18757763673526288444…68860929100303278079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.875 × 10⁹⁴(95-digit number)

18757763673526288444…68860929100303278081

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

3.751 × 10⁹⁴(95-digit number)

37515527347052576889…37721858200606556159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.751 × 10⁹⁴(95-digit number)

37515527347052576889…37721858200606556161

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

7.503 × 10⁹⁴(95-digit number)

75031054694105153778…75443716401213112319

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 256794

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 c42d29a2dbded92d06c42bb5e957f31310dfafc6379a8ca8e6fe8df6bbbbe58f

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 #256,794 on Chainz ↗