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Block #496,228

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 11:55:32 PM · Difficulty 10.7512 · 6,299,396 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aed116cfdd1a1c5a64f0c22d8d0ef792bbf6c3b68c5e64f91adb28181121c42b

View on Chainz ↗

Height

#496,228

Difficulty

10.751183

Transactions

Size

1.23 KB

Version

Bits

0ac04d80

Nonce

235,052,638

Timestamp

4/16/2014, 11:55:32 PM

Confirmations

6,299,396

Merkle Root

57bf0d171e67710f749011dcce56df701bab0b5b3bfaff318570bf1ef01ce7f5

Transactions (2)

Coinbase57d0f29db61527…c34bd1f18be1af

1 in → 1 out8.6600 XPM116 B

AbwWkWZt…kawDhufa

3711499deeb93b…3fdb2b95607aef

5 in → 14 out44.6600 XPM1.03 KB

AWCwAJy2…1ustaJof AWpN9SZ7…cfg39PDg AKgMuH2h…bnM6fTBV AH6atPTv…Wc9ye5Jg AJyGidYK…wD9VP2WE

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.

1.181 × 10⁹⁹(100-digit number)

11813635758449745244…12813811628035434880

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

1.181 × 10⁹⁹(100-digit number)

11813635758449745244…12813811628035434879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.181 × 10⁹⁹(100-digit number)

11813635758449745244…12813811628035434881

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

2.362 × 10⁹⁹(100-digit number)

23627271516899490488…25627623256070869759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.362 × 10⁹⁹(100-digit number)

23627271516899490488…25627623256070869761

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

4.725 × 10⁹⁹(100-digit number)

47254543033798980977…51255246512141739519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.725 × 10⁹⁹(100-digit number)

47254543033798980977…51255246512141739521

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

9.450 × 10⁹⁹(100-digit number)

94509086067597961954…02510493024283479039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.450 × 10⁹⁹(100-digit number)

94509086067597961954…02510493024283479041

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

1.890 × 10¹⁰⁰(101-digit number)

18901817213519592390…05020986048566958079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.890 × 10¹⁰⁰(101-digit number)

18901817213519592390…05020986048566958081

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 496228

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 aed116cfdd1a1c5a64f0c22d8d0ef792bbf6c3b68c5e64f91adb28181121c42b

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 #496,228 on Chainz ↗