Home/Chain Registry/Block #388,749

Block #388,749

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 1:11:29 AM · Difficulty 10.4149 · 6,415,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6b0b5a5b2d327800f069e69e5176d582a54014ae6ae8363851606685365acbc8

View on Chainz ↗

Height

#388,749

Difficulty

10.414879

Transactions

Size

1.22 KB

Version

Bits

0a6a358a

Nonce

4,759

Timestamp

2/4/2014, 1:11:29 AM

Confirmations

6,415,243

Merkle Root

b133e5704f04cf9ff8095c8b1898b7b7c19648ec2ac948ad0277c7bafae8ea5b

Transactions (3)

Coinbase940559f997ad13…c67410448c5fe3

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

0f3bed45fed38c…79d5dbb7b1a696

3 in → 2 out1087.9000 XPM521 B

AVwQuDSr…KsE1rjJF AU86iH4z…EqG91kPy

176da10f6de515…f1138906fd1c8b

3 in → 2 out3.0102 XPM523 B

AM7RBNfE…tepe5V7a AXVewGvF…GJwjnr25

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.

1.693 × 10⁹⁷(98-digit number)

16936527061744227637…86650704706315084480

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

1.693 × 10⁹⁷(98-digit number)

16936527061744227637…86650704706315084479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.693 × 10⁹⁷(98-digit number)

16936527061744227637…86650704706315084481

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

3.387 × 10⁹⁷(98-digit number)

33873054123488455274…73301409412630168959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.387 × 10⁹⁷(98-digit number)

33873054123488455274…73301409412630168961

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

6.774 × 10⁹⁷(98-digit number)

67746108246976910549…46602818825260337919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.774 × 10⁹⁷(98-digit number)

67746108246976910549…46602818825260337921

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

1.354 × 10⁹⁸(99-digit number)

13549221649395382109…93205637650520675839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.354 × 10⁹⁸(99-digit number)

13549221649395382109…93205637650520675841

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

2.709 × 10⁹⁸(99-digit number)

27098443298790764219…86411275301041351679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.709 × 10⁹⁸(99-digit number)

27098443298790764219…86411275301041351681

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 388749

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 6b0b5a5b2d327800f069e69e5176d582a54014ae6ae8363851606685365acbc8

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 #388,749 on Chainz ↗