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Block #494,440

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 4:25:54 AM · Difficulty 10.7183 · 6,320,615 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcd63cd720e7eac30e86d5a91c15ff9c9978fbc8f32d0e3029d710eae4cea2d0

View on Chainz ↗

Height

#494,440

Difficulty

10.718321

Transactions

Size

1.25 KB

Version

Bits

0ab7e3e6

Nonce

7,328,569

Timestamp

4/16/2014, 4:25:54 AM

Confirmations

6,320,615

Merkle Root

64efd610167273dcc9280658baf5783f852e0e47804360044dc7431102b3d00c

Transactions (4)

Coinbase1de8be2b432fda…e96493cae40f99

1 in → 1 out8.7200 XPM116 B

AbwWkWZt…kawDhufa

fc44dec622a7cc…ce51c00a231c21

1 in → 2 out380.3860 XPM224 B

AGf4bxML…tCqWcVMH AdWBpaDf…AnZQh7HZ

8234a65537c735…89eed998de4e34

3 in → 8 out26.3100 XPM625 B

AZgFHRrY…aQ2pD31y ATp7uG6c…qDLK4hNJ AeKNrjNj…1NEq95Ta AZqoSs9t…xTzRMnus AP6XU4Ao…mq8mf6N9

196db294bbc809…a9bca6019a192b

1 in → 2 out7.2053 XPM226 B

AMAxLjXk…843iHH6r ALHXSGQr…MmGHn1wJ

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.

4.985 × 10⁹⁹(100-digit number)

49851907529182421564…72633532325778670080

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

4.985 × 10⁹⁹(100-digit number)

49851907529182421564…72633532325778670079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.985 × 10⁹⁹(100-digit number)

49851907529182421564…72633532325778670081

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

9.970 × 10⁹⁹(100-digit number)

99703815058364843128…45267064651557340159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.970 × 10⁹⁹(100-digit number)

99703815058364843128…45267064651557340161

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

1.994 × 10¹⁰⁰(101-digit number)

19940763011672968625…90534129303114680319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.994 × 10¹⁰⁰(101-digit number)

19940763011672968625…90534129303114680321

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

3.988 × 10¹⁰⁰(101-digit number)

39881526023345937251…81068258606229360639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.988 × 10¹⁰⁰(101-digit number)

39881526023345937251…81068258606229360641

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

7.976 × 10¹⁰⁰(101-digit number)

79763052046691874503…62136517212458721279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.976 × 10¹⁰⁰(101-digit number)

79763052046691874503…62136517212458721281

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 494440

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 fcd63cd720e7eac30e86d5a91c15ff9c9978fbc8f32d0e3029d710eae4cea2d0

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 #494,440 on Chainz ↗

Block #494,440

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