Home/Chain Registry/Block #408,223

Block #408,223

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 12:19:25 PM · Difficulty 10.4313 · 6,418,202 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fa29370864232271365011ba4ee2e294fb33429311dccd00e3e1287a98426e08

View on Chainz ↗

Height

#408,223

Difficulty

10.431302

Transactions

Size

208 B

Version

Bits

0a6e69d3

Nonce

9,396

Timestamp

2/17/2014, 12:19:25 PM

Confirmations

6,418,202

Merkle Root

1e76f9fba6482ae2bada448fd761f55916e81291dc0becb8e1535d13a1991c05

Transactions (1)

Coinbase1e76f9fba6482a…535d13a1991c05

1 in → 1 out9.1800 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.

1.357 × 10¹⁰⁰(101-digit number)

13573764504906505412…07120895610305228800

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

1.357 × 10¹⁰⁰(101-digit number)

13573764504906505412…07120895610305228799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.357 × 10¹⁰⁰(101-digit number)

13573764504906505412…07120895610305228801

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

2.714 × 10¹⁰⁰(101-digit number)

27147529009813010825…14241791220610457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.714 × 10¹⁰⁰(101-digit number)

27147529009813010825…14241791220610457601

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

5.429 × 10¹⁰⁰(101-digit number)

54295058019626021651…28483582441220915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.429 × 10¹⁰⁰(101-digit number)

54295058019626021651…28483582441220915201

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

1.085 × 10¹⁰¹(102-digit number)

10859011603925204330…56967164882441830399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.085 × 10¹⁰¹(102-digit number)

10859011603925204330…56967164882441830401

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

2.171 × 10¹⁰¹(102-digit number)

21718023207850408660…13934329764883660799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.171 × 10¹⁰¹(102-digit number)

21718023207850408660…13934329764883660801

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 408223

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 fa29370864232271365011ba4ee2e294fb33429311dccd00e3e1287a98426e08

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 #408,223 on Chainz ↗

Block #408,223

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