Home/Chain Registry/Block #317,245

Block #317,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/17/2013, 1:25:17 PM · Difficulty 10.1566 · 6,509,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e06f695d78de37e049dddd6156e146198c92c9208b6adf9cf02fa9d8c8b4687

View on Chainz ↗

Height

#317,245

Difficulty

10.156567

Transactions

Size

1.08 KB

Version

Bits

0a2814ce

Nonce

22,750

Timestamp

12/17/2013, 1:25:17 PM

Confirmations

6,509,394

Merkle Root

86ffb368284fda9412eafb233074dcd9ad6775a3a15edb765b582aade9de5c94

Transactions (1)

Coinbase86ffb368284fda…582aade9de5c94

1 in → 28 out9.6600 XPM1015 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 Ae58nAEb…GFUA15fv Adp1wLWz…fELRJLx4 ALHbRxMJ…LEi9pifp

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.

4.333 × 10⁹²(93-digit number)

43335055925503027288…67959396062294910720

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

4.333 × 10⁹²(93-digit number)

43335055925503027288…67959396062294910719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.333 × 10⁹²(93-digit number)

43335055925503027288…67959396062294910721

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

8.667 × 10⁹²(93-digit number)

86670111851006054576…35918792124589821439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.667 × 10⁹²(93-digit number)

86670111851006054576…35918792124589821441

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

1.733 × 10⁹³(94-digit number)

17334022370201210915…71837584249179642879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.733 × 10⁹³(94-digit number)

17334022370201210915…71837584249179642881

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

3.466 × 10⁹³(94-digit number)

34668044740402421830…43675168498359285759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.466 × 10⁹³(94-digit number)

34668044740402421830…43675168498359285761

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

6.933 × 10⁹³(94-digit number)

69336089480804843660…87350336996718571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.933 × 10⁹³(94-digit number)

69336089480804843660…87350336996718571521

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 317245

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 5e06f695d78de37e049dddd6156e146198c92c9208b6adf9cf02fa9d8c8b4687

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 #317,245 on Chainz ↗

Block #317,245

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