Home/Chain Registry/Block #297,368

Block #297,368

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 1:49:33 PM · Difficulty 9.9920 · 6,494,555 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f96bfccdcfcab1439ee4fecf4146ede28c23cf7d575ee27500d84c12b7019fa1

View on Chainz ↗

Height

#297,368

Difficulty

9.991954

Transactions

Size

205 B

Version

Bits

09fdf0b7

Nonce

271,062

Timestamp

12/6/2013, 1:49:33 PM

Confirmations

6,494,555

Merkle Root

1bc844c01a007f914e150d7d597135252264fe468526370477656bc4f7330b30

Transactions (1)

Coinbase1bc844c01a007f…656bc4f7330b30

1 in → 1 out10.0000 XPM116 B

AcLBm5Z9…S683d7c3

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.

1.047 × 10⁹³(94-digit number)

10470635549216509013…75999587760063474680

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

1.047 × 10⁹³(94-digit number)

10470635549216509013…75999587760063474679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.047 × 10⁹³(94-digit number)

10470635549216509013…75999587760063474681

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

2.094 × 10⁹³(94-digit number)

20941271098433018027…51999175520126949359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.094 × 10⁹³(94-digit number)

20941271098433018027…51999175520126949361

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

4.188 × 10⁹³(94-digit number)

41882542196866036055…03998351040253898719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.188 × 10⁹³(94-digit number)

41882542196866036055…03998351040253898721

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

8.376 × 10⁹³(94-digit number)

83765084393732072110…07996702080507797439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.376 × 10⁹³(94-digit number)

83765084393732072110…07996702080507797441

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

1.675 × 10⁹⁴(95-digit number)

16753016878746414422…15993404161015594879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.675 × 10⁹⁴(95-digit number)

16753016878746414422…15993404161015594881

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 297368

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 f96bfccdcfcab1439ee4fecf4146ede28c23cf7d575ee27500d84c12b7019fa1

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 #297,368 on Chainz ↗