Block #327,602

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/24/2013, 4:22:40 PM · Difficulty 10.1747 · 6,481,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24fec4b52a5a037391632fe59d7bbb9802c82ef620c38e607e8ca5ac5285bd27

View on Chainz ↗

Height

#327,602

Difficulty

10.174671

Transactions

Size

1.01 KB

Version

Bits

0a2cb73e

Nonce

359,577

Timestamp

12/24/2013, 4:22:40 PM

Confirmations

6,481,745

Mined by

⛏️ aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

f865abb602e9e2d5aa24d21b60d50f7271bdff8b32ad4df05399e2bedc4991fc

Transactions (1)

Coinbasef865abb602e9e2…99e2bedc4991fc

1 in → 26 out9.6400 XPM947 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AYtDvcGs…VuAcA7m7 AKzkYQaQ…zR4FspJZ

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.

1.842 × 10⁹⁵(96-digit number)

18426884609161393363…50256037560299601919

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

1.842 × 10⁹⁵(96-digit number)

18426884609161393363…50256037560299601919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.842 × 10⁹⁵(96-digit number)

18426884609161393363…50256037560299601921

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

3.685 × 10⁹⁵(96-digit number)

36853769218322786726…00512075120599203839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.685 × 10⁹⁵(96-digit number)

36853769218322786726…00512075120599203841

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

7.370 × 10⁹⁵(96-digit number)

73707538436645573453…01024150241198407679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.370 × 10⁹⁵(96-digit number)

73707538436645573453…01024150241198407681

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

1.474 × 10⁹⁶(97-digit number)

14741507687329114690…02048300482396815359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.474 × 10⁹⁶(97-digit number)

14741507687329114690…02048300482396815361

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

2.948 × 10⁹⁶(97-digit number)

29483015374658229381…04096600964793630719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.948 × 10⁹⁶(97-digit number)

29483015374658229381…04096600964793630721

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 #327,602

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