Block #2,267,340

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/25/2017, 1:07:21 PM · Difficulty 10.9517 · 4,577,934 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16f2a851ae372a94667685b542feaca89d3b891e992084c08b2f9b8d078d3700

View on Chainz ↗

Height

#2,267,340

Difficulty

10.951736

Transactions

Size

426 B

Version

Bits

0af3a4fa

Nonce

570,784,299

Timestamp

8/25/2017, 1:07:21 PM

Confirmations

4,577,934

Mined by

⛏️ P2SHAR1aGzJEinsKC7FFBqXadRrDZJvdXvczqP

Merkle Root

35eb5c389bad05f168758d815d37eff520700d0a1c6a6078f833763d6f2371ba

Transactions (2)

Coinbase155e58d498ba9c…dbbc4ed2ad4676

1 in → 1 out8.3300 XPM110 B

AR1aGzJE…vdXvczqP

d8d304ace6d7ca…5e98a33380e8e0

1 in → 2 out4776.5033 XPM226 B

AeZWxMuu…BR6LRqdE ARKvy9es…ecWDqdwY

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.

1.150 × 10⁹⁵(96-digit number)

11502727897544390434…10329931798957360319

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

1.150 × 10⁹⁵(96-digit number)

11502727897544390434…10329931798957360319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.150 × 10⁹⁵(96-digit number)

11502727897544390434…10329931798957360321

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

2.300 × 10⁹⁵(96-digit number)

23005455795088780868…20659863597914720639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.300 × 10⁹⁵(96-digit number)

23005455795088780868…20659863597914720641

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

4.601 × 10⁹⁵(96-digit number)

46010911590177561737…41319727195829441279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.601 × 10⁹⁵(96-digit number)

46010911590177561737…41319727195829441281

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

9.202 × 10⁹⁵(96-digit number)

92021823180355123474…82639454391658882559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.202 × 10⁹⁵(96-digit number)

92021823180355123474…82639454391658882561

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

1.840 × 10⁹⁶(97-digit number)

18404364636071024694…65278908783317765119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.840 × 10⁹⁶(97-digit number)

18404364636071024694…65278908783317765121

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 #2,267,340

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