Block #328,909

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 2:57:37 PM · Difficulty 10.1670 · 6,487,618 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

88e2d960d994db16f34f49ff50583d627ff069b4b929105a5748e2f7972d5dd0

View on Chainz ↗

Height

#328,909

Difficulty

10.167029

Transactions

Size

970 B

Version

Bits

0a2ac265

Nonce

82,465

Timestamp

12/25/2013, 2:57:37 PM

Confirmations

6,487,618

Mined by

⛏️ aRHAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

52aa2fe4d830c5d981cfed51b176fb7b23470c353c44bb1536e167b64f851a7e

Transactions (1)

Coinbase52aa2fe4d830c5…e167b64f851a7e

1 in → 24 out9.6600 XPM879 B

AQwRN8bE…V8PsTcY9 AQ8QAT3J…rCFKuVbR Aac9Hjdg…P4ktypc3 AG5YAjec…VhA4Aeh1 AFutDVqJ…TJTJj6UF

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.

3.988 × 10⁹⁶(97-digit number)

39887327071441489497…58806788062531450879

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

3.988 × 10⁹⁶(97-digit number)

39887327071441489497…58806788062531450879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.988 × 10⁹⁶(97-digit number)

39887327071441489497…58806788062531450881

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

7.977 × 10⁹⁶(97-digit number)

79774654142882978994…17613576125062901759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.977 × 10⁹⁶(97-digit number)

79774654142882978994…17613576125062901761

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

1.595 × 10⁹⁷(98-digit number)

15954930828576595798…35227152250125803519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.595 × 10⁹⁷(98-digit number)

15954930828576595798…35227152250125803521

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

3.190 × 10⁹⁷(98-digit number)

31909861657153191597…70454304500251607039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.190 × 10⁹⁷(98-digit number)

31909861657153191597…70454304500251607041

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

6.381 × 10⁹⁷(98-digit number)

63819723314306383195…40908609000503214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.381 × 10⁹⁷(98-digit number)

63819723314306383195…40908609000503214081

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 #328,909

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