Home/Chain Registry/Block #267,337

Block #267,337

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 5:08:33 AM · Difficulty 9.9591 · 6,523,948 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a29aa52d41b6a6d029350e9c4fa17d0b3a8bdec37448725328d2e9eefe1c1914

View on Chainz ↗

Height

#267,337

Difficulty

9.959090

Transactions

Size

211 B

Version

Bits

09f586ef

Nonce

186

Timestamp

11/21/2013, 5:08:33 AM

Confirmations

6,523,948

Merkle Root

581c1b6cc0b9f1158c81663a0c3c0ecb78765e2453b8e0cd7f2cd196f51fffc6

Transactions (1)

Coinbase581c1b6cc0b9f1…2cd196f51fffc6

1 in → 1 out10.0700 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.

2.285 × 10¹⁰⁷(108-digit number)

22858453087269196036…00095328289054720000

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

2.285 × 10¹⁰⁷(108-digit number)

22858453087269196036…00095328289054719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.285 × 10¹⁰⁷(108-digit number)

22858453087269196036…00095328289054720001

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

4.571 × 10¹⁰⁷(108-digit number)

45716906174538392072…00190656578109439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.571 × 10¹⁰⁷(108-digit number)

45716906174538392072…00190656578109440001

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

9.143 × 10¹⁰⁷(108-digit number)

91433812349076784144…00381313156218879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.143 × 10¹⁰⁷(108-digit number)

91433812349076784144…00381313156218880001

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

1.828 × 10¹⁰⁸(109-digit number)

18286762469815356828…00762626312437759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.828 × 10¹⁰⁸(109-digit number)

18286762469815356828…00762626312437760001

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

3.657 × 10¹⁰⁸(109-digit number)

36573524939630713657…01525252624875519999

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 267337

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 a29aa52d41b6a6d029350e9c4fa17d0b3a8bdec37448725328d2e9eefe1c1914

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 #267,337 on Chainz ↗