Block #2,247,579

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/12/2017, 1:17:48 AM · Difficulty 10.9478 · 4,579,144 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d8b66df69719e381aa3cb9cd192a12c4a46af669719f6bbe07ee3f43fa2f398

View on Chainz ↗

Height

#2,247,579

Difficulty

10.947824

Transactions

Size

1.50 KB

Version

Bits

0af2a49e

Nonce

280,960,387

Timestamp

8/12/2017, 1:17:48 AM

Confirmations

4,579,144

Mined by

⛏️ P2SHAWp99go3gAANDkRJjggVh4jetA2Lqpqp56

Merkle Root

00809de324f82d5eec32f6053640e4d0c1f8752fbdec9675f8d5a3057462ff55

Transactions (3)

Coinbased2a7f8de3de36a…450122bf048980

1 in → 1 out8.3600 XPM110 B

AWp99go3…2Lqpqp56

f454439c4daf2d…ad3bb72d9a4955

1 in → 2 out68514.5369 XPM226 B

AbGujrpg…hWRmyVPB AXevUr5Z…4A3pZ1cY

756fafc5207d73…86721a17db9ba6

7 in → 2 out2000.0127 XPM1.09 KB

AVj7mp3X…Jue1KZ5z ARaNCeSx…b8M3uhxY

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.

1.573 × 10⁹⁸(99-digit number)

15731709066678507621…33996431862818897919

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

1.573 × 10⁹⁸(99-digit number)

15731709066678507621…33996431862818897919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.573 × 10⁹⁸(99-digit number)

15731709066678507621…33996431862818897921

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

3.146 × 10⁹⁸(99-digit number)

31463418133357015243…67992863725637795839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.146 × 10⁹⁸(99-digit number)

31463418133357015243…67992863725637795841

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

6.292 × 10⁹⁸(99-digit number)

62926836266714030486…35985727451275591679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.292 × 10⁹⁸(99-digit number)

62926836266714030486…35985727451275591681

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

1.258 × 10⁹⁹(100-digit number)

12585367253342806097…71971454902551183359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.258 × 10⁹⁹(100-digit number)

12585367253342806097…71971454902551183361

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

2.517 × 10⁹⁹(100-digit number)

25170734506685612194…43942909805102366719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.517 × 10⁹⁹(100-digit number)

25170734506685612194…43942909805102366721

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 #2,247,579

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