Block #2,781,693

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/6/2018, 12:39:49 PM · Difficulty 11.6498 · 4,028,645 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

30ebc12d8b29d617201fec517249b3776cae284aa08e36b1434cfdb0c7d6f8ca

View on Chainz ↗

Height

#2,781,693

Difficulty

11.649807

Transactions

Size

689 B

Version

Bits

0ba659bd

Nonce

60,441,562

Timestamp

8/6/2018, 12:39:49 PM

Confirmations

4,028,645

Mined by

⛏️ P2SHAV387rXVoBeuxJBbVUso2Jyfg13geH2U66

Merkle Root

2c93b3edc27d76000200726f88b40448fa93b6405f5f32a85d0216556ec56d35

Transactions (2)

Coinbase06f9817deced0e…c4509a0e825132

1 in → 1 out7.3700 XPM110 B

AV387rXV…3geH2U66

425edcbfef72df…ca0d83a24da5f3

3 in → 2 out11.4500 XPM487 B

AQe669ne…BLRSRycv AKD9LeNP…bQTn8mEf

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.

5.818 × 10⁹⁸(99-digit number)

58180182249185776670…41001422934155223039

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

5.818 × 10⁹⁸(99-digit number)

58180182249185776670…41001422934155223039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.818 × 10⁹⁸(99-digit number)

58180182249185776670…41001422934155223041

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

1.163 × 10⁹⁹(100-digit number)

11636036449837155334…82002845868310446079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.163 × 10⁹⁹(100-digit number)

11636036449837155334…82002845868310446081

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

2.327 × 10⁹⁹(100-digit number)

23272072899674310668…64005691736620892159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.327 × 10⁹⁹(100-digit number)

23272072899674310668…64005691736620892161

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

4.654 × 10⁹⁹(100-digit number)

46544145799348621336…28011383473241784319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.654 × 10⁹⁹(100-digit number)

46544145799348621336…28011383473241784321

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

9.308 × 10⁹⁹(100-digit number)

93088291598697242672…56022766946483568639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.308 × 10⁹⁹(100-digit number)

93088291598697242672…56022766946483568641

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

1.861 × 10¹⁰⁰(101-digit number)

18617658319739448534…12045533892967137279

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 #2,781,693

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