Block #342,458

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 2:19:12 AM · Difficulty 10.1598 · 6,466,292 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

26491995a799253f21aed6016a849cbcba39a5b2f3b755a819057c4f157a357e

View on Chainz ↗

Height

#342,458

Difficulty

10.159849

Transactions

Size

1.08 KB

Version

Bits

0a28ebd5

Nonce

9,495

Timestamp

1/4/2014, 2:19:12 AM

Confirmations

6,466,292

Mined by

⛏️ 9aRoAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

ba888f5b58a4fffd6d4134026d44a7f5b0bb18581671e8b73f61dabfd84be0a1

Transactions (1)

Coinbaseba888f5b58a4ff…61dabfd84be0a1

1 in → 28 out9.6500 XPM1015 B

AFutDVqJ…TJTJj6UF AQwRN8bE…V8PsTcY9 AYtDvcGs…VuAcA7m7 AQvZBsUo…hppgRZTJ AZemWJAo…6jhDtieG

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.

2.420 × 10⁹⁷(98-digit number)

24200981617202468140…01249729743961420799

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

2.420 × 10⁹⁷(98-digit number)

24200981617202468140…01249729743961420799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.420 × 10⁹⁷(98-digit number)

24200981617202468140…01249729743961420801

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

4.840 × 10⁹⁷(98-digit number)

48401963234404936280…02499459487922841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.840 × 10⁹⁷(98-digit number)

48401963234404936280…02499459487922841601

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

9.680 × 10⁹⁷(98-digit number)

96803926468809872561…04998918975845683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.680 × 10⁹⁷(98-digit number)

96803926468809872561…04998918975845683201

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

1.936 × 10⁹⁸(99-digit number)

19360785293761974512…09997837951691366399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.936 × 10⁹⁸(99-digit number)

19360785293761974512…09997837951691366401

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

3.872 × 10⁹⁸(99-digit number)

38721570587523949024…19995675903382732799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.872 × 10⁹⁸(99-digit number)

38721570587523949024…19995675903382732801

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 #342,458

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