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Block #399,184

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/11/2014, 6:53:11 AM · Difficulty 10.4196 · 6,414,974 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a78b6c29316914cca1f03003da0291e898e02cf820242c8e02ff64f8d6a5e23

View on Chainz ↗

Height

#399,184

Difficulty

10.419588

Transactions

Size

426 B

Version

Bits

0a6b6a20

Nonce

45,225

Timestamp

2/11/2014, 6:53:11 AM

Confirmations

6,414,974

Merkle Root

b19190b11038660962f85704daaa4aaaed8cc5ff7f6c46c5105bcf083619a4c1

Transactions (2)

Coinbase2d089e230db09c…f1fb11efe1654b

1 in → 1 out9.2100 XPM109 B

AcfVCq85…FVgVXmvr

3e60faae52755b…27bc0ef05a6fa4

1 in → 2 out16920.7280 XPM226 B

ARfQgDK4…Cq7aesAW AXjahksH…JGmxbTjZ

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.

1.664 × 10⁹⁶(97-digit number)

16644831750371016815…39702831402293816140

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

1.664 × 10⁹⁶(97-digit number)

16644831750371016815…39702831402293816139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.664 × 10⁹⁶(97-digit number)

16644831750371016815…39702831402293816141

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

3.328 × 10⁹⁶(97-digit number)

33289663500742033631…79405662804587632279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.328 × 10⁹⁶(97-digit number)

33289663500742033631…79405662804587632281

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

6.657 × 10⁹⁶(97-digit number)

66579327001484067262…58811325609175264559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.657 × 10⁹⁶(97-digit number)

66579327001484067262…58811325609175264561

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

1.331 × 10⁹⁷(98-digit number)

13315865400296813452…17622651218350529119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.331 × 10⁹⁷(98-digit number)

13315865400296813452…17622651218350529121

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

2.663 × 10⁹⁷(98-digit number)

26631730800593626904…35245302436701058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.663 × 10⁹⁷(98-digit number)

26631730800593626904…35245302436701058241

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 399184

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 8a78b6c29316914cca1f03003da0291e898e02cf820242c8e02ff64f8d6a5e23

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 #399,184 on Chainz ↗

Block #399,184

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