Home/Chain Registry/Block #416,196

Block #416,196

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/23/2014, 6:16:08 AM · Difficulty 10.4002 · 6,411,160 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef95fc50a49df444c7092a72d67ce84ddc2b27f05eef2e399e12a591e4ce2d07

View on Chainz ↗

Height

#416,196

Difficulty

10.400241

Transactions

Size

1.10 KB

Version

Bits

0a667639

Nonce

269,025

Timestamp

2/23/2014, 6:16:08 AM

Confirmations

6,411,160

Merkle Root

c125bfa85434723eedac131ade729d3eedc1c40896bce09f3218e59965f46057

Transactions (2)

Coinbase161c2fedff2d3a…bfaa299c808f1f

1 in → 23 out9.2296 XPM845 B

AHZUHC8g…t3rBwmSA AYtDvcGs…VuAcA7m7 AbBw3Mve…ej8uK4rz AQwRN8bE…V8PsTcY9 AGmDpQMh…8qfUtstd

9623e7f512abe7…92a8010e79bf12

1 in → 1 out1.5000 XPM192 B

AJ3BUQN9…YZwoT75f

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.

4.199 × 10⁹⁷(98-digit number)

41991408831426215316…87225120666165341840

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

4.199 × 10⁹⁷(98-digit number)

41991408831426215316…87225120666165341839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.199 × 10⁹⁷(98-digit number)

41991408831426215316…87225120666165341841

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

8.398 × 10⁹⁷(98-digit number)

83982817662852430633…74450241332330683679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.398 × 10⁹⁷(98-digit number)

83982817662852430633…74450241332330683681

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

1.679 × 10⁹⁸(99-digit number)

16796563532570486126…48900482664661367359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.679 × 10⁹⁸(99-digit number)

16796563532570486126…48900482664661367361

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

3.359 × 10⁹⁸(99-digit number)

33593127065140972253…97800965329322734719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.359 × 10⁹⁸(99-digit number)

33593127065140972253…97800965329322734721

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

6.718 × 10⁹⁸(99-digit number)

67186254130281944506…95601930658645469439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.718 × 10⁹⁸(99-digit number)

67186254130281944506…95601930658645469441

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 416196

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 ef95fc50a49df444c7092a72d67ce84ddc2b27f05eef2e399e12a591e4ce2d07

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 #416,196 on Chainz ↗

Block #416,196

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