Block #343,138

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/4/2014, 12:29:00 PM · Difficulty 10.1686 · 6,473,739 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d0eee8707a740a5a7dcbf60be5111151c060f54287c9ea3364f4350cc46c076d

View on Chainz ↗

Height

#343,138

Difficulty

10.168580

Transactions

Size

1.11 KB

Version

Bits

0a2b2815

Nonce

3,876

Timestamp

1/4/2014, 12:29:00 PM

Confirmations

6,473,739

Mined by

⛏️ P2SHAKMP2CVuYkMFM3HypE35aAQREnWohLx3P7

Merkle Root

a4ec96b9ad6269d8f1a2fadf8f6bc1882c9b3645c4bdf74cf5298c5335fadecf

Transactions (2)

Coinbase953ff8762c3619…e2a483a2605ba1

1 in → 1 out9.6700 XPM109 B

AKMP2CVu…WohLx3P7

2a961a157c1e16…cb6f123bc98b92

6 in → 1 out1.8500 XPM931 B

AUbCZ7rN…WM5oYpcb

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.

7.418 × 10⁹⁹(100-digit number)

74183047694467771488…14678702458250063999

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

7.418 × 10⁹⁹(100-digit number)

74183047694467771488…14678702458250063999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.418 × 10⁹⁹(100-digit number)

74183047694467771488…14678702458250064001

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

1.483 × 10¹⁰⁰(101-digit number)

14836609538893554297…29357404916500127999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.483 × 10¹⁰⁰(101-digit number)

14836609538893554297…29357404916500128001

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

2.967 × 10¹⁰⁰(101-digit number)

29673219077787108595…58714809833000255999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.967 × 10¹⁰⁰(101-digit number)

29673219077787108595…58714809833000256001

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

5.934 × 10¹⁰⁰(101-digit number)

59346438155574217190…17429619666000511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.934 × 10¹⁰⁰(101-digit number)

59346438155574217190…17429619666000512001

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

1.186 × 10¹⁰¹(102-digit number)

11869287631114843438…34859239332001023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.186 × 10¹⁰¹(102-digit number)

11869287631114843438…34859239332001024001

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 #343,138

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