Home/Chain Registry/Block #267,019

Block #267,019

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 9:54:40 PM · Difficulty 9.9600 · 6,524,611 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d379b34f127b1c46a2021a14eecf736f454500b0af7bbeb5300457fb3720930b

View on Chainz ↗

Height

#267,019

Difficulty

9.959985

Transactions

Size

428 B

Version

Bits

09f5c198

Nonce

122,350

Timestamp

11/20/2013, 9:54:40 PM

Confirmations

6,524,611

Merkle Root

ab045f58f1687dc8972bdd7c1c1d9ab5f91bf0123904c5d1e2825ff957aac350

Transactions (2)

Coinbase3aeba2975e9f34…88c1af043fead4

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

538f8ef63a89a2…97c3258c8bf4a5

1 in → 2 out1.1700 XPM227 B

AULdkAnL…9VpFJvWp AL48EMca…MMV6JRSc

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.

1.799 × 10⁹⁷(98-digit number)

17999964228789984410…86794987663378859520

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

1.799 × 10⁹⁷(98-digit number)

17999964228789984410…86794987663378859519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.799 × 10⁹⁷(98-digit number)

17999964228789984410…86794987663378859521

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

3.599 × 10⁹⁷(98-digit number)

35999928457579968820…73589975326757719039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.599 × 10⁹⁷(98-digit number)

35999928457579968820…73589975326757719041

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

7.199 × 10⁹⁷(98-digit number)

71999856915159937640…47179950653515438079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.199 × 10⁹⁷(98-digit number)

71999856915159937640…47179950653515438081

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

1.439 × 10⁹⁸(99-digit number)

14399971383031987528…94359901307030876159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.439 × 10⁹⁸(99-digit number)

14399971383031987528…94359901307030876161

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

2.879 × 10⁹⁸(99-digit number)

28799942766063975056…88719802614061752319

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 267019

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 d379b34f127b1c46a2021a14eecf736f454500b0af7bbeb5300457fb3720930b

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 #267,019 on Chainz ↗