Home/Chain Registry/Block #27,527

Block #27,527

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 9:08:34 AM · Difficulty 7.9791 · 6,762,497 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

804030073c241d05d1aea71292d21a05df3cae93a666579ddfc5b093d4870bb9

View on Chainz ↗

Height

#27,527

Difficulty

7.979111

Transactions

Size

198 B

Version

Bits

07faa703

Nonce

1,170

Timestamp

7/13/2013, 9:08:34 AM

Confirmations

6,762,497

Merkle Root

04ab1fbda2f9bd176fe48d4e1d2b8e8ffbbfd6b6846621d5e6147402258e657e

Transactions (1)

Coinbase04ab1fbda2f9bd…147402258e657e

1 in → 1 out15.6900 XPM109 B

AG5PqAZS…QUBH4xQv

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.

3.518 × 10⁹¹(92-digit number)

35180346765796167572…17143532474490255240

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

3.518 × 10⁹¹(92-digit number)

35180346765796167572…17143532474490255239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.518 × 10⁹¹(92-digit number)

35180346765796167572…17143532474490255241

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

7.036 × 10⁹¹(92-digit number)

70360693531592335145…34287064948980510479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.036 × 10⁹¹(92-digit number)

70360693531592335145…34287064948980510481

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

1.407 × 10⁹²(93-digit number)

14072138706318467029…68574129897961020959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.407 × 10⁹²(93-digit number)

14072138706318467029…68574129897961020961

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

2.814 × 10⁹²(93-digit number)

28144277412636934058…37148259795922041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.814 × 10⁹²(93-digit number)

28144277412636934058…37148259795922041921

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 27527

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 804030073c241d05d1aea71292d21a05df3cae93a666579ddfc5b093d4870bb9

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 #27,527 on Chainz ↗