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Block #2,646,891

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 2:30:11 PM · Difficulty 11.7559 · 4,186,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8643bd5158966bbfc6deef1aac95ef521f8740a80905f1839f705c1d46597cce

View on Chainz ↗

Height

#2,646,891

Difficulty

11.755850

Transactions

Size

427 B

Version

Bits

0bc17f67

Nonce

45,534,179

Timestamp

5/3/2018, 2:30:11 PM

Confirmations

4,186,361

Merkle Root

e14046407839334d4cdd548196ec5504c1d1079f9e757b9a62a59550e80e705c

Transactions (2)

Coinbase7cc0825130725f…a66ba88c8a533f

1 in → 1 out7.2300 XPM110 B

AdyyZS82…TqPXBsGR

08cb4c04ef8c38…0331637019dffa

1 in → 2 out5.3317 XPM226 B

AXp1ebhg…iLUCa8jU AJMrMUVA…XLVBXChy

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.

9.776 × 10⁹⁷(98-digit number)

97769310587397527331…97484629675170529280

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

9.776 × 10⁹⁷(98-digit number)

97769310587397527331…97484629675170529279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.776 × 10⁹⁷(98-digit number)

97769310587397527331…97484629675170529281

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

1.955 × 10⁹⁸(99-digit number)

19553862117479505466…94969259350341058559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.955 × 10⁹⁸(99-digit number)

19553862117479505466…94969259350341058561

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

3.910 × 10⁹⁸(99-digit number)

39107724234959010932…89938518700682117119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.910 × 10⁹⁸(99-digit number)

39107724234959010932…89938518700682117121

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

7.821 × 10⁹⁸(99-digit number)

78215448469918021865…79877037401364234239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.821 × 10⁹⁸(99-digit number)

78215448469918021865…79877037401364234241

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

1.564 × 10⁹⁹(100-digit number)

15643089693983604373…59754074802728468479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.564 × 10⁹⁹(100-digit number)

15643089693983604373…59754074802728468481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.128 × 10⁹⁹(100-digit number)

31286179387967208746…19508149605456936959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2646891

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 8643bd5158966bbfc6deef1aac95ef521f8740a80905f1839f705c1d46597cce

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 #2,646,891 on Chainz ↗

Block #2,646,891

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