Block #2,165,383

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2017, 3:38:59 AM · Difficulty 10.8984 · 4,661,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75313abbb41d19120b3a06e05da32a4c7e2ae9a16e8d6bf669d895a4b3b09285

View on Chainz ↗

Height

#2,165,383

Difficulty

10.898385

Transactions

Size

426 B

Version

Bits

0ae5fc8e

Nonce

9,927,735

Timestamp

6/18/2017, 3:38:59 AM

Confirmations

4,661,584

Mined by

⛏️ P2SHAU7hZySZWDSP88tHwip3w6LnRkcS82Rf5w

Merkle Root

f06cb15a3f63bf1405a2ebb094da534b89cad9ee4b13f71b783e54976528dc25

Transactions (2)

Coinbasea2ccb3dbc7663f…e095f83d19604a

1 in → 1 out8.4200 XPM110 B

AU7hZySZ…cS82Rf5w

12dc8103cc6662…705412dc1b2d12

1 in → 2 out18.9801 XPM226 B

AHL3YjAe…mNZMCQnk ATbraDFx…5zidfhST

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.

1.060 × 10⁹⁴(95-digit number)

10601346320371617284…37645978401561326149

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

1.060 × 10⁹⁴(95-digit number)

10601346320371617284…37645978401561326149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.060 × 10⁹⁴(95-digit number)

10601346320371617284…37645978401561326151

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

2.120 × 10⁹⁴(95-digit number)

21202692640743234568…75291956803122652299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.120 × 10⁹⁴(95-digit number)

21202692640743234568…75291956803122652301

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

4.240 × 10⁹⁴(95-digit number)

42405385281486469137…50583913606245304599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.240 × 10⁹⁴(95-digit number)

42405385281486469137…50583913606245304601

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

8.481 × 10⁹⁴(95-digit number)

84810770562972938275…01167827212490609199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.481 × 10⁹⁴(95-digit number)

84810770562972938275…01167827212490609201

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

1.696 × 10⁹⁵(96-digit number)

16962154112594587655…02335654424981218399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.696 × 10⁹⁵(96-digit number)

16962154112594587655…02335654424981218401

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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer

Block #2,165,383

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