Block #466,041

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 9:37:53 PM · Difficulty 10.4224 · 6,337,377 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3316a33c46f6c1e8e0f0942a3e6ac1ec2cd03466903627e46bbc07ec0b038726

View on Chainz ↗

Height

#466,041

Difficulty

10.422429

Transactions

Size

578 B

Version

Bits

0a6c2453

Nonce

130,814

Timestamp

3/29/2014, 9:37:53 PM

Confirmations

6,337,377

Mined by

⛏️ P2SHAPi8Jc5hHXRPX4cYctszGF9N4WRFfBgREn

Merkle Root

804ad4ed0910382625fe0a302d5cafb8fa6d2741e20dbef3cbe4498937ba8186

Transactions (2)

Coinbase0e51b08833d072…fe9540ee87c205

1 in → 1 out9.2000 XPM112 B

APi8Jc5h…RFfBgREn

24dfc1d28e34e5…1a4150be0eb088

2 in → 2 out3.0632 XPM375 B

Af68qJko…bRWfunjf AGerLemW…yHec6Vit

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.

9.064 × 10⁹⁷(98-digit number)

90644198286287998935…48928543024874514559

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

9.064 × 10⁹⁷(98-digit number)

90644198286287998935…48928543024874514559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.064 × 10⁹⁷(98-digit number)

90644198286287998935…48928543024874514561

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

1.812 × 10⁹⁸(99-digit number)

18128839657257599787…97857086049749029119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.812 × 10⁹⁸(99-digit number)

18128839657257599787…97857086049749029121

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

3.625 × 10⁹⁸(99-digit number)

36257679314515199574…95714172099498058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.625 × 10⁹⁸(99-digit number)

36257679314515199574…95714172099498058241

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

7.251 × 10⁹⁸(99-digit number)

72515358629030399148…91428344198996116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.251 × 10⁹⁸(99-digit number)

72515358629030399148…91428344198996116481

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

1.450 × 10⁹⁹(100-digit number)

14503071725806079829…82856688397992232959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.450 × 10⁹⁹(100-digit number)

14503071725806079829…82856688397992232961

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