Home/Chain Registry/Block #442,122

Block #442,122

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/13/2014, 2:39:59 PM · Difficulty 10.3524 · 6,370,500 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3be07c5fd810d168a14dd5aa53bb86e7fb6d4dcc481ec65aec81ce2c62904b59

View on Chainz ↗

Height

#442,122

Difficulty

10.352428

Transactions

Size

209 B

Version

Bits

0a5a38b8

Nonce

8,237

Timestamp

3/13/2014, 2:39:59 PM

Confirmations

6,370,500

Merkle Root

59a129500cdd18c03e7662dfe3bfde8b70d1357c0259902e9aa1b009853487d2

Transactions (1)

Coinbase59a129500cdd18…a1b009853487d2

1 in → 1 out9.3200 XPM116 B

AbwWkWZt…kawDhufa

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.

8.368 × 10¹⁰¹(102-digit number)

83682341384510977293…31328612831450890240

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

8.368 × 10¹⁰¹(102-digit number)

83682341384510977293…31328612831450890239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.368 × 10¹⁰¹(102-digit number)

83682341384510977293…31328612831450890241

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

1.673 × 10¹⁰²(103-digit number)

16736468276902195458…62657225662901780479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.673 × 10¹⁰²(103-digit number)

16736468276902195458…62657225662901780481

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

3.347 × 10¹⁰²(103-digit number)

33472936553804390917…25314451325803560959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.347 × 10¹⁰²(103-digit number)

33472936553804390917…25314451325803560961

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

6.694 × 10¹⁰²(103-digit number)

66945873107608781834…50628902651607121919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.694 × 10¹⁰²(103-digit number)

66945873107608781834…50628902651607121921

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

1.338 × 10¹⁰³(104-digit number)

13389174621521756366…01257805303214243839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.338 × 10¹⁰³(104-digit number)

13389174621521756366…01257805303214243841

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 442122

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 3be07c5fd810d168a14dd5aa53bb86e7fb6d4dcc481ec65aec81ce2c62904b59

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 #442,122 on Chainz ↗

Block #442,122

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