Home/Chain Registry/Block #311,129

Block #311,129

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 10:25:17 AM · Difficulty 9.9954 · 6,514,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a1cb7ce7dee31132098826f1cdd210d531efc4426e58b13cd41dd0b4716ddd9

View on Chainz ↗

Height

#311,129

Difficulty

9.995372

Transactions

Size

1.01 KB

Version

Bits

09fed0ac

Nonce

44,627

Timestamp

12/14/2013, 10:25:17 AM

Confirmations

6,514,482

Merkle Root

9c3000b600597969ca9c4ebf964a438fb1ce5a05d8cf0fd630c60d7d05c6396c

Transactions (1)

Coinbase9c3000b6005979…c60d7d05c6396c

1 in → 26 out9.9900 XPM947 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AMdvB6BS…DPq9FYdA AM6QcXma…gSEqm47e ALeiLa7r…gwdjnkKw

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.

2.030 × 10⁹¹(92-digit number)

20302076069537346892…68390675304518492800

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

2.030 × 10⁹¹(92-digit number)

20302076069537346892…68390675304518492799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.030 × 10⁹¹(92-digit number)

20302076069537346892…68390675304518492801

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

4.060 × 10⁹¹(92-digit number)

40604152139074693784…36781350609036985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.060 × 10⁹¹(92-digit number)

40604152139074693784…36781350609036985601

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

8.120 × 10⁹¹(92-digit number)

81208304278149387569…73562701218073971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.120 × 10⁹¹(92-digit number)

81208304278149387569…73562701218073971201

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

1.624 × 10⁹²(93-digit number)

16241660855629877513…47125402436147942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.624 × 10⁹²(93-digit number)

16241660855629877513…47125402436147942401

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

3.248 × 10⁹²(93-digit number)

32483321711259755027…94250804872295884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.248 × 10⁹²(93-digit number)

32483321711259755027…94250804872295884801

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 311129

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 3a1cb7ce7dee31132098826f1cdd210d531efc4426e58b13cd41dd0b4716ddd9

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 #311,129 on Chainz ↗

Block #311,129

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