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Block #266,946

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/20/2013, 8:45:52 PM · Difficulty 9.9599 · 6,559,641 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f581ee8a39ccab8118e9254084042516d3d6f640e495c1941e149fb0d27f43bd

View on Chainz ↗

Height

#266,946

Difficulty

9.959942

Transactions

Size

6.35 KB

Version

Bits

09f5bebb

Nonce

28,253

Timestamp

11/20/2013, 8:45:52 PM

Confirmations

6,559,641

Merkle Root

4c13019026dd959156d0540dffccff6515436f1cff7f553bf3b656666e655f5c

Transactions (4)

Coinbase937d776eb54aeb…757aa1db004e82

1 in → 1 out10.1600 XPM109 B

AQJ25GX9…hkswJFfn

71ea112e214a36…1bd60985a62d0c

6 in → 2 out1000.0114 XPM965 B

AJw6wABH…AWVeG5P3 AYC33k1z…1seVHqi4

5bcd06c7bd1f34…e4203c6f1d12d8

34 in → 2 out4.4799 XPM4.99 KB

AZMg2G66…n73rFPb2 ATES7xpE…wssPdRPC

d07176a3717e61…17ffc1edb2672a

1 in → 2 out6.7665 XPM227 B

ARyHReP1…RCDqPuwD AeKNrjNj…1NEq95Ta

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.

5.795 × 10⁹⁴(95-digit number)

57956906323381891311…24943325331037571120

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

5.795 × 10⁹⁴(95-digit number)

57956906323381891311…24943325331037571119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.795 × 10⁹⁴(95-digit number)

57956906323381891311…24943325331037571121

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

1.159 × 10⁹⁵(96-digit number)

11591381264676378262…49886650662075142239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.159 × 10⁹⁵(96-digit number)

11591381264676378262…49886650662075142241

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

2.318 × 10⁹⁵(96-digit number)

23182762529352756524…99773301324150284479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.318 × 10⁹⁵(96-digit number)

23182762529352756524…99773301324150284481

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

4.636 × 10⁹⁵(96-digit number)

46365525058705513049…99546602648300568959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.636 × 10⁹⁵(96-digit number)

46365525058705513049…99546602648300568961

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

9.273 × 10⁹⁵(96-digit number)

92731050117411026098…99093205296601137919

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 266946

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 f581ee8a39ccab8118e9254084042516d3d6f640e495c1941e149fb0d27f43bd

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 #266,946 on Chainz ↗

Block #266,946

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