Home/Chain Registry/Block #425,501

Block #425,501

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/1/2014, 11:28:53 PM · Difficulty 10.3589 · 6,370,487 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9aa9b1a991b7a159806af52a22b42735486f1cb1061ab772dc8f66e577e96de0

View on Chainz ↗

Height

#425,501

Difficulty

10.358887

Transactions

Size

969 B

Version

Bits

0a5be002

Nonce

10,662

Timestamp

3/1/2014, 11:28:53 PM

Confirmations

6,370,487

Merkle Root

167bcd164dbd5f124ecba73983855a0c073058b866e653a2911b80b8ffaaae01

Transactions (1)

Coinbase167bcd164dbd5f…1b80b8ffaaae01

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

9.810 × 10⁹³(94-digit number)

98105250270847032298…39245686979974013760

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

9.810 × 10⁹³(94-digit number)

98105250270847032298…39245686979974013759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.810 × 10⁹³(94-digit number)

98105250270847032298…39245686979974013761

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

1.962 × 10⁹⁴(95-digit number)

19621050054169406459…78491373959948027519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.962 × 10⁹⁴(95-digit number)

19621050054169406459…78491373959948027521

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

3.924 × 10⁹⁴(95-digit number)

39242100108338812919…56982747919896055039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.924 × 10⁹⁴(95-digit number)

39242100108338812919…56982747919896055041

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

7.848 × 10⁹⁴(95-digit number)

78484200216677625839…13965495839792110079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.848 × 10⁹⁴(95-digit number)

78484200216677625839…13965495839792110081

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

1.569 × 10⁹⁵(96-digit number)

15696840043335525167…27930991679584220159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.569 × 10⁹⁵(96-digit number)

15696840043335525167…27930991679584220161

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 425501

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 9aa9b1a991b7a159806af52a22b42735486f1cb1061ab772dc8f66e577e96de0

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 #425,501 on Chainz ↗