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Block #395,279

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/8/2014, 2:38:48 PM · Difficulty 10.4124 · 6,421,594 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f704ba71724d45dca0ea60824b4e7c43dab6fd73c11d12991a384f00306749f4

View on Chainz ↗

Height

#395,279

Difficulty

10.412392

Transactions

Size

10.13 KB

Version

Bits

0a69928b

Nonce

33,173,439

Timestamp

2/8/2014, 2:38:48 PM

Confirmations

6,421,594

Merkle Root

4ab748fdd0bfb11d16c6970e36690f7da27c77e1b463b23c98cdd585d87b2da9

Transactions (3)

Coinbaseb20d916f00300a…9c23e40b98d8ec

1 in → 1 out9.3300 XPM109 B

ANFCCaDm…oVcF6imK

3e50a260c56655…198b488f165899

63 in → 2 out20.3091 XPM9.18 KB

AHjxjypg…BfqPH2LH AYQAaJdL…Ak3Zv8Qm

2f6ad9dadeb514…a1bd853891d53d

4 in → 7 out18.8344 XPM772 B

AKcu64aE…A3Vqf3cv AK3XRe91…xA8wva2G AdjVuW2o…RiqZiW4R AVMRAzar…3e1KTuWa AHCuz9P2…41tUcRdy

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.

4.531 × 10⁹⁷(98-digit number)

45318804730901464252…73664857733375221760

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

4.531 × 10⁹⁷(98-digit number)

45318804730901464252…73664857733375221759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.531 × 10⁹⁷(98-digit number)

45318804730901464252…73664857733375221761

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

9.063 × 10⁹⁷(98-digit number)

90637609461802928504…47329715466750443519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.063 × 10⁹⁷(98-digit number)

90637609461802928504…47329715466750443521

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

1.812 × 10⁹⁸(99-digit number)

18127521892360585700…94659430933500887039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.812 × 10⁹⁸(99-digit number)

18127521892360585700…94659430933500887041

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

3.625 × 10⁹⁸(99-digit number)

36255043784721171401…89318861867001774079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.625 × 10⁹⁸(99-digit number)

36255043784721171401…89318861867001774081

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

7.251 × 10⁹⁸(99-digit number)

72510087569442342803…78637723734003548159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.251 × 10⁹⁸(99-digit number)

72510087569442342803…78637723734003548161

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 395279

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 f704ba71724d45dca0ea60824b4e7c43dab6fd73c11d12991a384f00306749f4

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 #395,279 on Chainz ↗

Block #395,279

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