Home/Chain Registry/Block #297,951

Block #297,951

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 11:34:43 PM · Difficulty 9.9920 · 6,494,057 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a800c47eede9d4bdf93830d9f8f8471c8256d2a42ac5dc0926c17f05946b0e7

View on Chainz ↗

Height

#297,951

Difficulty

9.991975

Transactions

Size

18.34 KB

Version

Bits

09fdf218

Nonce

1,323,640

Timestamp

12/6/2013, 11:34:43 PM

Confirmations

6,494,057

Merkle Root

0473dda8632993abcb0206ea982010f010afb0a3b9fb8644a2a74bceb4533cc4

Transactions (2)

Coinbase74493d7d4d01ce…7eca8c4d5314e3

1 in → 1 out10.1900 XPM110 B

AeKNrjNj…1NEq95Ta

fac7b2e2186b2e…627d6cffa5440a

125 in → 2 out45.0100 XPM18.15 KB

AS6JkeGs…9vcbqANK AVF6Bzao…RBYRgBgP

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.

6.623 × 10⁹²(93-digit number)

66233084929550273572…31138916072989828800

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

6.623 × 10⁹²(93-digit number)

66233084929550273572…31138916072989828799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.623 × 10⁹²(93-digit number)

66233084929550273572…31138916072989828801

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

1.324 × 10⁹³(94-digit number)

13246616985910054714…62277832145979657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.324 × 10⁹³(94-digit number)

13246616985910054714…62277832145979657601

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

2.649 × 10⁹³(94-digit number)

26493233971820109428…24555664291959315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.649 × 10⁹³(94-digit number)

26493233971820109428…24555664291959315201

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

5.298 × 10⁹³(94-digit number)

52986467943640218857…49111328583918630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.298 × 10⁹³(94-digit number)

52986467943640218857…49111328583918630401

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

1.059 × 10⁹⁴(95-digit number)

10597293588728043771…98222657167837260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.059 × 10⁹⁴(95-digit number)

10597293588728043771…98222657167837260801

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 297951

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 6a800c47eede9d4bdf93830d9f8f8471c8256d2a42ac5dc0926c17f05946b0e7

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 #297,951 on Chainz ↗