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Block #399,673

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 1:46:28 PM · Difficulty 10.4292 · 6,442,933 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

529bde77ea88326030b6f281fb15aa86e283a443feace57dcf149e09a40ffb60

View on Chainz ↗

Height

#399,673

Difficulty

10.429152

Transactions

Size

970 B

Version

Bits

0a6ddce6

Nonce

447,500

Timestamp

2/11/2014, 1:46:28 PM

Confirmations

6,442,933

Merkle Root

3b5c3dcb296c083a323d96984b76b447c53c61938a47d16f70c2ed86524f5699

Transactions (1)

Coinbase3b5c3dcb296c08…c2ed86524f5699

1 in → 24 out9.1800 XPM879 B

AQvZBsUo…hppgRZTJ AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 ALqxX1WA…hsKjbnXn

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.

8.111 × 10⁹⁶(97-digit number)

81111583828065492396…34067469758038686720

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

8.111 × 10⁹⁶(97-digit number)

81111583828065492396…34067469758038686719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.111 × 10⁹⁶(97-digit number)

81111583828065492396…34067469758038686721

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

1.622 × 10⁹⁷(98-digit number)

16222316765613098479…68134939516077373439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.622 × 10⁹⁷(98-digit number)

16222316765613098479…68134939516077373441

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

3.244 × 10⁹⁷(98-digit number)

32444633531226196958…36269879032154746879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.244 × 10⁹⁷(98-digit number)

32444633531226196958…36269879032154746881

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

6.488 × 10⁹⁷(98-digit number)

64889267062452393917…72539758064309493759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.488 × 10⁹⁷(98-digit number)

64889267062452393917…72539758064309493761

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

1.297 × 10⁹⁸(99-digit number)

12977853412490478783…45079516128618987519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.297 × 10⁹⁸(99-digit number)

12977853412490478783…45079516128618987521

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 399673

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 529bde77ea88326030b6f281fb15aa86e283a443feace57dcf149e09a40ffb60

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 #399,673 on Chainz ↗

Block #399,673

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