Home/Chain Registry/Block #274,427

Block #274,427

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 7:10:02 AM · Difficulty 9.9574 · 6,526,391 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d867f7ba21700ebe61942a3b8461230d8256c2ddef9b8b0b1ced4e371fef02bc

View on Chainz ↗

Height

#274,427

Difficulty

9.957390

Transactions

Size

391 B

Version

Bits

09f51780

Nonce

104,078

Timestamp

11/26/2013, 7:10:02 AM

Confirmations

6,526,391

Merkle Root

caee51ef6b51b1791a9ba9dae21469fb3b982f44e72bbea272c0616488af7908

Transactions (2)

Coinbase4a5db06da74fde…e353b20750a763

1 in → 1 out10.0800 XPM110 B

AeKNrjNj…1NEq95Ta

275c7d18fa26c4…a2a6477c39d541

1 in → 2 out10.1337 XPM191 B

AKN6pNCw…MeATKM2o ATzbJAUo…g1oc9dnz

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.

4.482 × 10⁹³(94-digit number)

44822850702294748450…97750240520139785400

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

4.482 × 10⁹³(94-digit number)

44822850702294748450…97750240520139785399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.482 × 10⁹³(94-digit number)

44822850702294748450…97750240520139785401

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

8.964 × 10⁹³(94-digit number)

89645701404589496901…95500481040279570799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.964 × 10⁹³(94-digit number)

89645701404589496901…95500481040279570801

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

1.792 × 10⁹⁴(95-digit number)

17929140280917899380…91000962080559141599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.792 × 10⁹⁴(95-digit number)

17929140280917899380…91000962080559141601

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

3.585 × 10⁹⁴(95-digit number)

35858280561835798760…82001924161118283199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.585 × 10⁹⁴(95-digit number)

35858280561835798760…82001924161118283201

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

7.171 × 10⁹⁴(95-digit number)

71716561123671597520…64003848322236566399

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 274427

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 d867f7ba21700ebe61942a3b8461230d8256c2ddef9b8b0b1ced4e371fef02bc

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 #274,427 on Chainz ↗