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Block #1,854,415

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/18/2016, 7:12:55 AM · Difficulty 10.6493 · 4,985,731 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3c1900895fe5e90f618e12b483e050c1318c84f5c132a4b8a9d9d98e4273c107

View on Chainz ↗

Height

#1,854,415

Difficulty

10.649279

Transactions

Size

425 B

Version

Bits

0aa63727

Nonce

1,397,699,388

Timestamp

11/18/2016, 7:12:55 AM

Confirmations

4,985,731

Merkle Root

d9d2b23f27f54a61e161e1542d78e06f0d4862bca00d5f245aa49cf333ae56f8

Transactions (2)

Coinbasef4da495c292638…1010f55c2d96c0

1 in → 1 out8.8100 XPM109 B

ALY5vQZR…FWXZTzTQ

dc03be93b9aac1…d60c6eb561ef7d

1 in → 2 out0.2535 XPM226 B

AUVyeEGr…cvxG3GKM AG91YFmA…bBTTFTsf

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.

1.980 × 10⁹⁴(95-digit number)

19803370288202995258…69161597614502952960

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

1.980 × 10⁹⁴(95-digit number)

19803370288202995258…69161597614502952959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.980 × 10⁹⁴(95-digit number)

19803370288202995258…69161597614502952961

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

3.960 × 10⁹⁴(95-digit number)

39606740576405990516…38323195229005905919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.960 × 10⁹⁴(95-digit number)

39606740576405990516…38323195229005905921

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

7.921 × 10⁹⁴(95-digit number)

79213481152811981033…76646390458011811839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.921 × 10⁹⁴(95-digit number)

79213481152811981033…76646390458011811841

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

1.584 × 10⁹⁵(96-digit number)

15842696230562396206…53292780916023623679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.584 × 10⁹⁵(96-digit number)

15842696230562396206…53292780916023623681

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

3.168 × 10⁹⁵(96-digit number)

31685392461124792413…06585561832047247359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.168 × 10⁹⁵(96-digit number)

31685392461124792413…06585561832047247361

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 1854415

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 3c1900895fe5e90f618e12b483e050c1318c84f5c132a4b8a9d9d98e4273c107

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 #1,854,415 on Chainz ↗

Block #1,854,415

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