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Block #407,949

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/17/2014, 8:05:01 AM · Difficulty 10.4293 · 6,408,834 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

abbae7a69eea24702094d6810e2c90f62a91886da1b4e1f0a431145ee875a738

View on Chainz ↗

Height

#407,949

Difficulty

10.429265

Transactions

Size

435 B

Version

Bits

0a6de457

Nonce

3,435

Timestamp

2/17/2014, 8:05:01 AM

Confirmations

6,408,834

Merkle Root

5acc12f835036dfe8c93872ab9ad544374761f9defe6a4ba72b2c1502377f96e

Transactions (2)

Coinbase7754aed34a0270…6ac51d57739ed2

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

be821618ff0308…972acc05380103

1 in → 2 out2.5667 XPM227 B

AM69wz8L…XaqhCSw6 ANEEDkQH…bHnEyrDc

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.

3.657 × 10⁹⁸(99-digit number)

36577291377246408255…18834768376247055880

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

3.657 × 10⁹⁸(99-digit number)

36577291377246408255…18834768376247055879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.657 × 10⁹⁸(99-digit number)

36577291377246408255…18834768376247055881

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

7.315 × 10⁹⁸(99-digit number)

73154582754492816510…37669536752494111759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.315 × 10⁹⁸(99-digit number)

73154582754492816510…37669536752494111761

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

1.463 × 10⁹⁹(100-digit number)

14630916550898563302…75339073504988223519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.463 × 10⁹⁹(100-digit number)

14630916550898563302…75339073504988223521

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

2.926 × 10⁹⁹(100-digit number)

29261833101797126604…50678147009976447039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.926 × 10⁹⁹(100-digit number)

29261833101797126604…50678147009976447041

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

5.852 × 10⁹⁹(100-digit number)

58523666203594253208…01356294019952894079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.852 × 10⁹⁹(100-digit number)

58523666203594253208…01356294019952894081

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 407949

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 abbae7a69eea24702094d6810e2c90f62a91886da1b4e1f0a431145ee875a738

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 #407,949 on Chainz ↗

Block #407,949

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