Home/Chain Registry/Block #1,425,416

Block #1,425,416

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2016, 6:17:45 PM · Difficulty 10.7660 · 5,407,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c30e64237202e252c76104c3d9c2bb6e52843b73449979a27193c0424794958

View on Chainz ↗

Height

#1,425,416

Difficulty

10.766017

Transactions

Size

5.54 KB

Version

Bits

0ac419ae

Nonce

858,011,757

Timestamp

1/23/2016, 6:17:45 PM

Confirmations

5,407,900

Merkle Root

97c2e589f5f8e325e9587a2015745d7862b7aeff070cceb28294b61c75b4f684

Transactions (4)

Coinbase21392ed45cc145…ed4b0d296c3c9d

1 in → 1 out8.6700 XPM109 B

AMfJpwDF…CrR4mQ4Q

989ab182f9309b…cb00cc3181dd8b

1 in → 45 out98.7856 XPM1.65 KB

AZiFi5Xe…2mZ2aske AK4pu9aP…L3oUb29v AcccAgdq…fokh3B4o APvWjwxP…6RpqMAq1 ALj7fhin…d1uVPKJq

5b8870cede0283…dde4fada6dd9e2

1 in → 51 out63.7890 XPM1.85 KB

AXisyknQ…ZTUGCTrx AYkHZmcd…RirttaWu AR948gVq…y7uqPqsK APP5tctX…gsDaJjj9 AG7ofBFD…XDMSyNJA

b4eef00c72e51e…0dec8e2788305e

1 in → 51 out11.7393 XPM1.85 KB

AXvEQxdT…JiotQyuV Aabrvz97…BNqKPEQ1 AXUaQQJX…ytdHmeGA AU4atFeB…9HbnrKMf ATkiCeum…91r8eHmY

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.

5.329 × 10⁹⁷(98-digit number)

53294052887881657133…12180771623498219520

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

5.329 × 10⁹⁷(98-digit number)

53294052887881657133…12180771623498219519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.329 × 10⁹⁷(98-digit number)

53294052887881657133…12180771623498219521

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

1.065 × 10⁹⁸(99-digit number)

10658810577576331426…24361543246996439039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.065 × 10⁹⁸(99-digit number)

10658810577576331426…24361543246996439041

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

2.131 × 10⁹⁸(99-digit number)

21317621155152662853…48723086493992878079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.131 × 10⁹⁸(99-digit number)

21317621155152662853…48723086493992878081

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

4.263 × 10⁹⁸(99-digit number)

42635242310305325706…97446172987985756159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.263 × 10⁹⁸(99-digit number)

42635242310305325706…97446172987985756161

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

8.527 × 10⁹⁸(99-digit number)

85270484620610651412…94892345975971512319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.527 × 10⁹⁸(99-digit number)

85270484620610651412…94892345975971512321

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 1425416

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 1c30e64237202e252c76104c3d9c2bb6e52843b73449979a27193c0424794958

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 #1,425,416 on Chainz ↗

Block #1,425,416

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