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Block #255,568

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 8:11:39 AM · Difficulty 9.9745 · 6,569,442 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2267ee2d91095021e2a4dd8cd9ad692fb77907d470b81f28d42ee89598abc06b

View on Chainz ↗

Height

#255,568

Difficulty

9.974454

Transactions

Size

787 B

Version

Bits

09f975ca

Nonce

183,294

Timestamp

11/11/2013, 8:11:39 AM

Confirmations

6,569,442

Merkle Root

9b6c54454a2b2382eec4173e59a09db610cf9202015311a292139fb5abdda5d1

Transactions (3)

Coinbasea28fe8d4fb90b5…e8218b8737489c

1 in → 1 out10.0600 XPM110 B

AeKNrjNj…1NEq95Ta

2de103c0ab130b…8c693d0fd3f34e

1 in → 4 out15.8892 XPM293 B

AGKsGytR…WW4z5VzK AdCUnJu7…3ug23bwQ AZ1BTjCh…JnBxH9Dq AKK61RDB…3DWa1N7M

bde30a9db6099f…abd48d1e84a204

1 in → 4 out15.1515 XPM294 B

AGKsGytR…WW4z5VzK ATY1vA2D…kg9YHXCy AKK61RDB…3DWa1N7M AZ1BTjCh…JnBxH9Dq

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.

1.463 × 10⁹⁵(96-digit number)

14638223306664006782…02862851453572812200

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

1.463 × 10⁹⁵(96-digit number)

14638223306664006782…02862851453572812199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.463 × 10⁹⁵(96-digit number)

14638223306664006782…02862851453572812201

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

2.927 × 10⁹⁵(96-digit number)

29276446613328013565…05725702907145624399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.927 × 10⁹⁵(96-digit number)

29276446613328013565…05725702907145624401

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

5.855 × 10⁹⁵(96-digit number)

58552893226656027130…11451405814291248799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.855 × 10⁹⁵(96-digit number)

58552893226656027130…11451405814291248801

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

1.171 × 10⁹⁶(97-digit number)

11710578645331205426…22902811628582497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.171 × 10⁹⁶(97-digit number)

11710578645331205426…22902811628582497601

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

2.342 × 10⁹⁶(97-digit number)

23421157290662410852…45805623257164995199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.342 × 10⁹⁶(97-digit number)

23421157290662410852…45805623257164995201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 255568

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 2267ee2d91095021e2a4dd8cd9ad692fb77907d470b81f28d42ee89598abc06b

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 #255,568 on Chainz ↗

Block #255,568

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