Home/Chain Registry/Block #331,105

Block #331,105

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 3:34:42 AM · Difficulty 10.1654 · 6,485,577 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13bbd84a9402f7cf924d2e00905922917e49f048b9cd56dfff3fb7b04816a1d3

View on Chainz ↗

Height

#331,105

Difficulty

10.165430

Transactions

Size

1.05 KB

Version

Bits

0a2a59a6

Nonce

875,118

Timestamp

12/27/2013, 3:34:42 AM

Confirmations

6,485,577

Merkle Root

11ea72639e2b17bb27afce8a433294b40e246a003e0c04b8e3064a726eba4a54

Transactions (1)

Coinbase11ea72639e2b17…064a726eba4a54

1 in → 27 out9.6600 XPM981 B

AFutDVqJ…TJTJj6UF AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Aac9Hjdg…P4ktypc3

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.

3.935 × 10⁹⁴(95-digit number)

39350466933858600808…08651597115197142400

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

3.935 × 10⁹⁴(95-digit number)

39350466933858600808…08651597115197142399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.935 × 10⁹⁴(95-digit number)

39350466933858600808…08651597115197142401

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

7.870 × 10⁹⁴(95-digit number)

78700933867717201617…17303194230394284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.870 × 10⁹⁴(95-digit number)

78700933867717201617…17303194230394284801

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

1.574 × 10⁹⁵(96-digit number)

15740186773543440323…34606388460788569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.574 × 10⁹⁵(96-digit number)

15740186773543440323…34606388460788569601

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

3.148 × 10⁹⁵(96-digit number)

31480373547086880647…69212776921577139199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.148 × 10⁹⁵(96-digit number)

31480373547086880647…69212776921577139201

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

6.296 × 10⁹⁵(96-digit number)

62960747094173761294…38425553843154278399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.296 × 10⁹⁵(96-digit number)

62960747094173761294…38425553843154278401

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 331105

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 13bbd84a9402f7cf924d2e00905922917e49f048b9cd56dfff3fb7b04816a1d3

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 #331,105 on Chainz ↗

Block #331,105

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