Block #355,598

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2014, 6:19:19 AM · Difficulty 10.3617 · 6,448,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

170537183aa21d7c41b6c062b4363ce1ccb746ec3c630325c1485ffb3a4e0fe4

View on Chainz ↗

Height

#355,598

Difficulty

10.361682

Transactions

Size

972 B

Version

Bits

0a5c9730

Nonce

415,802

Timestamp

1/12/2014, 6:19:19 AM

Confirmations

6,448,184

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

aa179835df1acd4037d759b69757fcaba1921f8871b76b0a37ca0aff4d80a2e1

Transactions (2)

Coinbaseec5d43679fce22…3a1b0c16cda0a4

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

d10fe9ba652417…15a487ca9787c0

4 in → 7 out19.1261 XPM771 B

Abjxw224…p8Ae4YKZ AZSsb8zU…b9zoouHo Ad15gKfJ…iZMkZt6b AL2v7PE7…5Q5y9E81 AbYTcX8d…nkbCya5K

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.

2.869 × 10⁹⁷(98-digit number)

28699135979034430479…79628000452082561439

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

2.869 × 10⁹⁷(98-digit number)

28699135979034430479…79628000452082561439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.869 × 10⁹⁷(98-digit number)

28699135979034430479…79628000452082561441

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

5.739 × 10⁹⁷(98-digit number)

57398271958068860959…59256000904165122879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.739 × 10⁹⁷(98-digit number)

57398271958068860959…59256000904165122881

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

1.147 × 10⁹⁸(99-digit number)

11479654391613772191…18512001808330245759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.147 × 10⁹⁸(99-digit number)

11479654391613772191…18512001808330245761

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

2.295 × 10⁹⁸(99-digit number)

22959308783227544383…37024003616660491519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.295 × 10⁹⁸(99-digit number)

22959308783227544383…37024003616660491521

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

4.591 × 10⁹⁸(99-digit number)

45918617566455088767…74048007233320983039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.591 × 10⁹⁸(99-digit number)

45918617566455088767…74048007233320983041

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