Home/Chain Registry/Block #1,497,842

Block #1,497,842

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2016, 1:12:29 PM · Difficulty 10.6454 · 5,329,113 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f792302ae23b360866634cef33489d0e0621c83c1c16ccd7ee4bbb082592a5db

View on Chainz ↗

Height

#1,497,842

Difficulty

10.645408

Transactions

Size

1.15 KB

Version

Bits

0aa53974

Nonce

440,172,392

Timestamp

3/15/2016, 1:12:29 PM

Confirmations

5,329,113

Merkle Root

2c1711ef4e584eec074c15a6ff0e3983afa8434212b07f8ff82f77164470a386

Transactions (2)

Coinbase4a4fbcf098c83b…df5e0585c5d0df

1 in → 1 out8.8200 XPM109 B

AMQJE53y…5RusqSE5

fd8eaffa9da377…325a16b49100f0

1 in → 24 out98.0071 XPM973 B

AVKkBCXd…3uqD9wkx AcFf68GJ…soMGkgc2 AYn2K6Kr…4LVQJafS AeVwC1gJ…5jcsgvkt Ace41asT…Agjmepno

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.

4.447 × 10⁹⁶(97-digit number)

44470089599120885902…77167252188537640960

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

4.447 × 10⁹⁶(97-digit number)

44470089599120885902…77167252188537640959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.447 × 10⁹⁶(97-digit number)

44470089599120885902…77167252188537640961

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

8.894 × 10⁹⁶(97-digit number)

88940179198241771804…54334504377075281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.894 × 10⁹⁶(97-digit number)

88940179198241771804…54334504377075281921

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

1.778 × 10⁹⁷(98-digit number)

17788035839648354360…08669008754150563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.778 × 10⁹⁷(98-digit number)

17788035839648354360…08669008754150563841

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

3.557 × 10⁹⁷(98-digit number)

35576071679296708721…17338017508301127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.557 × 10⁹⁷(98-digit number)

35576071679296708721…17338017508301127681

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

7.115 × 10⁹⁷(98-digit number)

71152143358593417443…34676035016602255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.115 × 10⁹⁷(98-digit number)

71152143358593417443…34676035016602255361

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 1497842

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 f792302ae23b360866634cef33489d0e0621c83c1c16ccd7ee4bbb082592a5db

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 #1,497,842 on Chainz ↗

Block #1,497,842

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