Block #348,896

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2014, 1:57:06 AM · Difficulty 10.2676 · 6,468,046 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e687b95b35b5993deadd53ede1d30c670082459de0ffdbf51edd00ef6c7f57e7

View on Chainz ↗

Height

#348,896

Difficulty

10.267605

Transactions

Size

834 B

Version

Bits

0a4481c4

Nonce

4,560

Timestamp

1/8/2014, 1:57:06 AM

Confirmations

6,468,046

Mined by

⛏️ RaRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

ab2968b65c97264118595e958e5106b651c8a128b625a3d3a29c021dc8293ee9

Transactions (1)

Coinbaseab2968b65c9726…9c021dc8293ee9

1 in → 20 out9.4700 XPM743 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR AL8CJrXc…ReWqhicJ ARSeozDw…C9HtARnj

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.

1.380 × 10⁹⁸(99-digit number)

13804466956631752292…68279150448455085229

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

1.380 × 10⁹⁸(99-digit number)

13804466956631752292…68279150448455085229

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.380 × 10⁹⁸(99-digit number)

13804466956631752292…68279150448455085231

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

2.760 × 10⁹⁸(99-digit number)

27608933913263504584…36558300896910170459

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.760 × 10⁹⁸(99-digit number)

27608933913263504584…36558300896910170461

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

5.521 × 10⁹⁸(99-digit number)

55217867826527009169…73116601793820340919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.521 × 10⁹⁸(99-digit number)

55217867826527009169…73116601793820340921

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

1.104 × 10⁹⁹(100-digit number)

11043573565305401833…46233203587640681839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.104 × 10⁹⁹(100-digit number)

11043573565305401833…46233203587640681841

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

2.208 × 10⁹⁹(100-digit number)

22087147130610803667…92466407175281363679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.208 × 10⁹⁹(100-digit number)

22087147130610803667…92466407175281363681

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 #348,896

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