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Block #476,633

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 10:58:42 PM · Difficulty 10.4752 · 6,348,338 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

867f3dea79554f3f0a75064f062d1449b80a115ee8269fdb3bc2e4d616e43200

View on Chainz ↗

Height

#476,633

Difficulty

10.475151

Transactions

Size

209 B

Version

Bits

0a79a379

Nonce

10,062

Timestamp

4/5/2014, 10:58:42 PM

Confirmations

6,348,338

Merkle Root

4d556daa612541f5c6d0b3fe4506ff1ad2370113718db65cc2fb7cb2ebeb549b

Transactions (1)

Coinbase4d556daa612541…fb7cb2ebeb549b

1 in → 1 out9.1000 XPM116 B

AbwWkWZt…kawDhufa

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.

3.506 × 10¹⁰²(103-digit number)

35061128483964091144…21576130962575689600

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

3.506 × 10¹⁰²(103-digit number)

35061128483964091144…21576130962575689599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.506 × 10¹⁰²(103-digit number)

35061128483964091144…21576130962575689601

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

7.012 × 10¹⁰²(103-digit number)

70122256967928182289…43152261925151379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.012 × 10¹⁰²(103-digit number)

70122256967928182289…43152261925151379201

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

1.402 × 10¹⁰³(104-digit number)

14024451393585636457…86304523850302758399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.402 × 10¹⁰³(104-digit number)

14024451393585636457…86304523850302758401

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

2.804 × 10¹⁰³(104-digit number)

28048902787171272915…72609047700605516799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.804 × 10¹⁰³(104-digit number)

28048902787171272915…72609047700605516801

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

5.609 × 10¹⁰³(104-digit number)

56097805574342545831…45218095401211033599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.609 × 10¹⁰³(104-digit number)

56097805574342545831…45218095401211033601

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 476633

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 867f3dea79554f3f0a75064f062d1449b80a115ee8269fdb3bc2e4d616e43200

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 #476,633 on Chainz ↗

Block #476,633

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