Home/Chain Registry/Block #310,386

Block #310,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/14/2013, 1:25:34 AM · Difficulty 9.9952 · 6,482,199 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3282f95f8e5c1bac5ca3d5de6e2e2224dd20ca0837bf909386f0f7134ad2a94

View on Chainz ↗

Height

#310,386

Difficulty

9.995159

Transactions

Size

202 B

Version

Bits

09fec2b7

Nonce

124,406

Timestamp

12/14/2013, 1:25:34 AM

Confirmations

6,482,199

Merkle Root

2fc1ee43b04c63b98f506d69d5386400ba4a35c1f8c7168bd1779e034e75796c

Transactions (1)

Coinbase2fc1ee43b04c63…779e034e75796c

1 in → 1 out9.9900 XPM110 B

AeKNrjNj…1NEq95Ta

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.

2.226 × 10⁹⁹(100-digit number)

22263920225794433961…43096480457915422720

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

2.226 × 10⁹⁹(100-digit number)

22263920225794433961…43096480457915422719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.226 × 10⁹⁹(100-digit number)

22263920225794433961…43096480457915422721

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

4.452 × 10⁹⁹(100-digit number)

44527840451588867923…86192960915830845439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.452 × 10⁹⁹(100-digit number)

44527840451588867923…86192960915830845441

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

8.905 × 10⁹⁹(100-digit number)

89055680903177735847…72385921831661690879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.905 × 10⁹⁹(100-digit number)

89055680903177735847…72385921831661690881

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

1.781 × 10¹⁰⁰(101-digit number)

17811136180635547169…44771843663323381759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.781 × 10¹⁰⁰(101-digit number)

17811136180635547169…44771843663323381761

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

3.562 × 10¹⁰⁰(101-digit number)

35622272361271094338…89543687326646763519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.562 × 10¹⁰⁰(101-digit number)

35622272361271094338…89543687326646763521

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 310386

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 e3282f95f8e5c1bac5ca3d5de6e2e2224dd20ca0837bf909386f0f7134ad2a94

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 #310,386 on Chainz ↗