Home/Chain Registry/Block #351,684

Block #351,684

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 8:41:22 PM · Difficulty 10.3000 · 6,462,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d5bff860c92f64c3c81454c7ce9f8d76b91287194dcdbb5d62de5dbb6d8d2f97

View on Chainz ↗

Height

#351,684

Difficulty

10.300024

Transactions

Size

1.61 KB

Version

Bits

0a4cce59

Nonce

93,842

Timestamp

1/9/2014, 8:41:22 PM

Confirmations

6,462,246

Merkle Root

ebd1cfbb65c54b4d1e34ba921f097d4740aac4d90e3abca25c9e9155cb790275

Transactions (4)

Coinbasefb0ba234d546a8…13686bfacbc403

1 in → 24 out9.4100 XPM879 B

AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR ARjgNH4d…BU7Drh7C AL8CJrXc…ReWqhicJ ARSeozDw…C9HtARnj

1e27db839385a0…3c63a852ec8e83

1 in → 2 out9.4800 XPM225 B

AHPTgojf…3W7gWnxq AW5FBmQ8…S9fc4Kp6

974031c15391e5…cf2b2eb7cfca05

1 in → 2 out9.4800 XPM226 B

AKredzXk…9XrijgMp AP1T4SwJ…Td3DhxBj

1d334c90a2bbda…ece5eb256c9f7f

1 in → 2 out9.4800 XPM227 B

AP7tMsv6…PvazezvK AGdCh2Qb…cpGouWxn

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.

1.111 × 10⁹²(93-digit number)

11118196965372935945…78050040111763382400

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

1.111 × 10⁹²(93-digit number)

11118196965372935945…78050040111763382399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.111 × 10⁹²(93-digit number)

11118196965372935945…78050040111763382401

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

2.223 × 10⁹²(93-digit number)

22236393930745871890…56100080223526764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.223 × 10⁹²(93-digit number)

22236393930745871890…56100080223526764801

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

4.447 × 10⁹²(93-digit number)

44472787861491743781…12200160447053529599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.447 × 10⁹²(93-digit number)

44472787861491743781…12200160447053529601

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

8.894 × 10⁹²(93-digit number)

88945575722983487563…24400320894107059199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.894 × 10⁹²(93-digit number)

88945575722983487563…24400320894107059201

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

1.778 × 10⁹³(94-digit number)

17789115144596697512…48800641788214118399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.778 × 10⁹³(94-digit number)

17789115144596697512…48800641788214118401

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 351684

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 d5bff860c92f64c3c81454c7ce9f8d76b91287194dcdbb5d62de5dbb6d8d2f97

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 #351,684 on Chainz ↗

Block #351,684

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