Block #328,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 3:27:48 AM · Difficulty 10.1712 · 6,478,764 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7aace78231e4b1a6faa1dcb8ed0ba3b5fd2f28f72f786d4707e7aa9f52ebb06

View on Chainz ↗

Height

#328,245

Difficulty

10.171188

Transactions

Size

1.08 KB

Version

Bits

0a2bd2f4

Nonce

62,616

Timestamp

12/25/2013, 3:27:48 AM

Confirmations

6,478,764

Mined by

⛏️ 5aRPAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

27b14a7d74aa82c7d52420835a44fada232f972fcc0195f0a71d625e4e6a054f

Transactions (1)

Coinbase27b14a7d74aa82…1d625e4e6a054f

1 in → 28 out9.6300 XPM1015 B

Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AWXYBWKP…qQAoisBJ AWQyM49v…zN9UeNMm AJzWx2VD…j4ZSMit5

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.

9.108 × 10⁹⁷(98-digit number)

91086210371453114853…60306998936780992799

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

9.108 × 10⁹⁷(98-digit number)

91086210371453114853…60306998936780992799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.108 × 10⁹⁷(98-digit number)

91086210371453114853…60306998936780992801

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

1.821 × 10⁹⁸(99-digit number)

18217242074290622970…20613997873561985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.821 × 10⁹⁸(99-digit number)

18217242074290622970…20613997873561985601

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

3.643 × 10⁹⁸(99-digit number)

36434484148581245941…41227995747123971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.643 × 10⁹⁸(99-digit number)

36434484148581245941…41227995747123971201

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

7.286 × 10⁹⁸(99-digit number)

72868968297162491882…82455991494247942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.286 × 10⁹⁸(99-digit number)

72868968297162491882…82455991494247942401

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

1.457 × 10⁹⁹(100-digit number)

14573793659432498376…64911982988495884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.457 × 10⁹⁹(100-digit number)

14573793659432498376…64911982988495884801

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 #328,245

Cookie Preferences