Block #339,588

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 5:27:31 AM · Difficulty 10.1257 · 6,471,520 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24f13b2707d4bd35144649edd324db34467c2d565de63109685e1c5eaf11d588

View on Chainz ↗

Height

#339,588

Difficulty

10.125689

Transactions

Size

1.01 KB

Version

Bits

0a202d21

Nonce

201,998

Timestamp

1/2/2014, 5:27:31 AM

Confirmations

6,471,520

Mined by

⛏️ .aR3AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

1a3f79fc46bde31b923489711661d5f5c4a69df6a70c433851d6c78a21b8fdfe

Transactions (1)

Coinbase1a3f79fc46bde3…d6c78a21b8fdfe

1 in → 26 out9.7400 XPM947 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 AP5UvYhU…vLTDwkdA

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.

2.163 × 10⁹³(94-digit number)

21634047951856888264…13815410182022469119

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

2.163 × 10⁹³(94-digit number)

21634047951856888264…13815410182022469119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.163 × 10⁹³(94-digit number)

21634047951856888264…13815410182022469121

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

4.326 × 10⁹³(94-digit number)

43268095903713776529…27630820364044938239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.326 × 10⁹³(94-digit number)

43268095903713776529…27630820364044938241

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

8.653 × 10⁹³(94-digit number)

86536191807427553059…55261640728089876479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.653 × 10⁹³(94-digit number)

86536191807427553059…55261640728089876481

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

1.730 × 10⁹⁴(95-digit number)

17307238361485510611…10523281456179752959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.730 × 10⁹⁴(95-digit number)

17307238361485510611…10523281456179752961

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

3.461 × 10⁹⁴(95-digit number)

34614476722971021223…21046562912359505919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.461 × 10⁹⁴(95-digit number)

34614476722971021223…21046562912359505921

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 #339,588

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