Home/Chain Registry/Block #275,074

Block #275,074

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 1:28:15 PM · Difficulty 9.9596 · 6,516,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cfb099ef8d6fe0cd926ad022b75d5a09697bab0865b4a3f96d640e6e9420d5b9

View on Chainz ↗

Height

#275,074

Difficulty

9.959618

Transactions

Size

1.08 KB

Version

Bits

09f5a98d

Nonce

22,712

Timestamp

11/26/2013, 1:28:15 PM

Confirmations

6,516,035

Merkle Root

46d5792883503f019f441ea507b3fd19b27f9efb7efa7a979018b1ff1a858d24

Transactions (1)

Coinbase46d5792883503f…18b1ff1a858d24

1 in → 28 out10.0500 XPM1015 B

AapjFG3p…HDiQzMr5 ANHbaxZp…XjnHCJJs AdHMGs8Y…dkXgZCKv AWVYhu22…btbWLPGx AQYsYcmZ…YFxxZBLN

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.

8.403 × 10⁸⁹(90-digit number)

84039108888255075376…14485986869021271780

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

8.403 × 10⁸⁹(90-digit number)

84039108888255075376…14485986869021271779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.403 × 10⁸⁹(90-digit number)

84039108888255075376…14485986869021271781

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

1.680 × 10⁹⁰(91-digit number)

16807821777651015075…28971973738042543559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.680 × 10⁹⁰(91-digit number)

16807821777651015075…28971973738042543561

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

3.361 × 10⁹⁰(91-digit number)

33615643555302030150…57943947476085087119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.361 × 10⁹⁰(91-digit number)

33615643555302030150…57943947476085087121

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

6.723 × 10⁹⁰(91-digit number)

67231287110604060301…15887894952170174239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.723 × 10⁹⁰(91-digit number)

67231287110604060301…15887894952170174241

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

1.344 × 10⁹¹(92-digit number)

13446257422120812060…31775789904340348479

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 275074

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 cfb099ef8d6fe0cd926ad022b75d5a09697bab0865b4a3f96d640e6e9420d5b9

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 #275,074 on Chainz ↗