Block #328,425

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 7:07:21 AM · Difficulty 10.1647 · 6,479,756 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e6f9059ac8645eaee99915ff1b6b2a7583a06ea2a397652d579d254b344aada

View on Chainz ↗

Height

#328,425

Difficulty

10.164734

Transactions

Size

1.08 KB

Version

Bits

0a2a2bfb

Nonce

411,222

Timestamp

12/25/2013, 7:07:21 AM

Confirmations

6,479,756

Mined by

⛏️ aRAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

7a6e47dbd3b02330e1fb58ed91a5f9a14e4573c78cefb6918f02eaf103cf632b

Transactions (1)

Coinbase7a6e47dbd3b023…02eaf103cf632b

1 in → 28 out9.6400 XPM1015 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AG5YAjec…VhA4Aeh1 Ad9pSzHt…cpJ3y2zz APeshfYV…3PKcKMKH

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.

2.890 × 10¹⁰³(104-digit number)

28906432548928244603…48994592255279806719

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

2.890 × 10¹⁰³(104-digit number)

28906432548928244603…48994592255279806719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.890 × 10¹⁰³(104-digit number)

28906432548928244603…48994592255279806721

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

5.781 × 10¹⁰³(104-digit number)

57812865097856489206…97989184510559613439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.781 × 10¹⁰³(104-digit number)

57812865097856489206…97989184510559613441

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

1.156 × 10¹⁰⁴(105-digit number)

11562573019571297841…95978369021119226879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.156 × 10¹⁰⁴(105-digit number)

11562573019571297841…95978369021119226881

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

2.312 × 10¹⁰⁴(105-digit number)

23125146039142595682…91956738042238453759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.312 × 10¹⁰⁴(105-digit number)

23125146039142595682…91956738042238453761

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

4.625 × 10¹⁰⁴(105-digit number)

46250292078285191365…83913476084476907519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.625 × 10¹⁰⁴(105-digit number)

46250292078285191365…83913476084476907521

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 #328,425

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