Block #2,165,622

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/18/2017, 7:30:04 AM · Difficulty 10.8985 · 4,651,815 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d65ccb2cdbef560a49ae21c50388bf5df7f4525e2b463d25c23481dc2ef95c3

View on Chainz ↗

Height

#2,165,622

Difficulty

10.898535

Transactions

Size

1.86 KB

Version

Bits

0ae60669

Nonce

1,056,952,936

Timestamp

6/18/2017, 7:30:04 AM

Confirmations

4,651,815

Mined by

⛏️ P2SHAKZCTo7Yysi7TTNteMabMtsGirgiTLMU8Y

Merkle Root

08191864940199d713a90d7abb599148db41729af4247f71d04e90c6d3a0c1ee

Transactions (2)

Coinbase235d0ea33a2e89…297366e43bf0da

1 in → 1 out8.4400 XPM109 B

AKZCTo7Y…giTLMU8Y

24bda1fc9d1942…ad524ca241ec84

11 in → 2 out7421.0000 XPM1.67 KB

ANr6pCrE…r8E74V74 AMswnAHY…UJkVubnD

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.

5.692 × 10⁹¹(92-digit number)

56925813796962931390…09674518889451774779

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

5.692 × 10⁹¹(92-digit number)

56925813796962931390…09674518889451774779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.692 × 10⁹¹(92-digit number)

56925813796962931390…09674518889451774781

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

1.138 × 10⁹²(93-digit number)

11385162759392586278…19349037778903549559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.138 × 10⁹²(93-digit number)

11385162759392586278…19349037778903549561

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

2.277 × 10⁹²(93-digit number)

22770325518785172556…38698075557807099119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.277 × 10⁹²(93-digit number)

22770325518785172556…38698075557807099121

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

4.554 × 10⁹²(93-digit number)

45540651037570345112…77396151115614198239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.554 × 10⁹²(93-digit number)

45540651037570345112…77396151115614198241

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

9.108 × 10⁹²(93-digit number)

91081302075140690224…54792302231228396479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.108 × 10⁹²(93-digit number)

91081302075140690224…54792302231228396481

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 #2,165,622

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