Block #367,841

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 8:41:21 AM · Difficulty 10.4359 · 6,449,843 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

117ba7f370fb504762eb7319ee24855f6fb51d8b5180107693b2725206e5f566

View on Chainz ↗

Height

#367,841

Difficulty

10.435924

Transactions

Size

2.32 KB

Version

Bits

0a6f98af

Nonce

25,378

Timestamp

1/20/2014, 8:41:21 AM

Confirmations

6,449,843

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9e28c1b6bd0b42c2bc7b9e231f96b5792cf6fb99d891fa0351caba89bca0dd72

Transactions (3)

Coinbaseae8d9e850a10fc…1f4189d7e56154

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

c18dfbb09f8f65…519886b1db2e27

13 in → 2 out130.2877 XPM1.96 KB

AYfr8Wfq…bPzPSyTL AcEUjB8T…7y8mLUDZ

3eb163de4d0796…bb49971f67b6ce

1 in → 1 out9.2000 XPM158 B

ARrVNVAk…DrtNokCL

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.

2.858 × 10¹⁰³(104-digit number)

28588997942459644745…96879651424973414399

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

2.858 × 10¹⁰³(104-digit number)

28588997942459644745…96879651424973414399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.858 × 10¹⁰³(104-digit number)

28588997942459644745…96879651424973414401

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

5.717 × 10¹⁰³(104-digit number)

57177995884919289490…93759302849946828799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.717 × 10¹⁰³(104-digit number)

57177995884919289490…93759302849946828801

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

1.143 × 10¹⁰⁴(105-digit number)

11435599176983857898…87518605699893657599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.143 × 10¹⁰⁴(105-digit number)

11435599176983857898…87518605699893657601

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

2.287 × 10¹⁰⁴(105-digit number)

22871198353967715796…75037211399787315199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.287 × 10¹⁰⁴(105-digit number)

22871198353967715796…75037211399787315201

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

4.574 × 10¹⁰⁴(105-digit number)

45742396707935431592…50074422799574630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.574 × 10¹⁰⁴(105-digit number)

45742396707935431592…50074422799574630401

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 #367,841

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