Block #2,280,342

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/3/2017, 6:43:25 AM · Difficulty 10.9560 · 4,561,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d66f1e894af23aa6613912585b011d2ba5005078abf480382da854454e50e44b

View on Chainz ↗

Height

#2,280,342

Difficulty

10.956023

Transactions

Size

1.86 KB

Version

Bits

0af4bdee

Nonce

42,976,315

Timestamp

9/3/2017, 6:43:25 AM

Confirmations

4,561,496

Mined by

⛏️ P2SHAT64dzRhwPamjW1LLoqrpvtQBmxnLCBbSf

Merkle Root

1efdffb7292c0700f0b62c8a19a669b7cc6389493834a63ea7482eec33b8c230

Transactions (2)

Coinbase47c7acf7ae0fd2…bcad9d250be326

1 in → 1 out8.3400 XPM109 B

AT64dzRh…xnLCBbSf

53e7ca09514c93…6bd40dfb9fc338

11 in → 2 out691.6785 XPM1.67 KB

AQmMKmSM…qsSQy3cC ATkWXYfG…DMV5btdf

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.

1.862 × 10⁹⁵(96-digit number)

18624218076587822915…97402208392218785279

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

1.862 × 10⁹⁵(96-digit number)

18624218076587822915…97402208392218785279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.862 × 10⁹⁵(96-digit number)

18624218076587822915…97402208392218785281

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

3.724 × 10⁹⁵(96-digit number)

37248436153175645830…94804416784437570559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.724 × 10⁹⁵(96-digit number)

37248436153175645830…94804416784437570561

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

7.449 × 10⁹⁵(96-digit number)

74496872306351291661…89608833568875141119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.449 × 10⁹⁵(96-digit number)

74496872306351291661…89608833568875141121

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

1.489 × 10⁹⁶(97-digit number)

14899374461270258332…79217667137750282239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.489 × 10⁹⁶(97-digit number)

14899374461270258332…79217667137750282241

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

2.979 × 10⁹⁶(97-digit number)

29798748922540516664…58435334275500564479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.979 × 10⁹⁶(97-digit number)

29798748922540516664…58435334275500564481

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

5.959 × 10⁹⁶(97-digit number)

59597497845081033328…16870668551001128959

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.

★★★☆☆

Rarity

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,280,342

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