Block #430,524

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/5/2014, 1:33:17 PM · Difficulty 10.3442 · 6,379,538 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e9e83accbefedee51be9982484b36a560a6a1109ae792b17b6b26ab4c512db7c

View on Chainz ↗

Height

#430,524

Difficulty

10.344200

Transactions

Size

902 B

Version

Bits

0a581d86

Nonce

270,078

Timestamp

3/5/2014, 1:33:17 PM

Confirmations

6,379,538

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

30b9e44bb6a2d6abc6f1ef2b40fb7e971b91978c2a9dd795658c2b1aecf2eca0

Transactions (1)

Coinbase30b9e44bb6a2d6…8c2b1aecf2eca0

1 in → 22 out9.3300 XPM811 B

AdFLJFhb…bsaVkAyh AUzEPJFG…kYkA5U9V Acs9SHrk…QJSB8SFG AGz9gyZW…bo8NYQpw AMW1p9oT…2TzdaZxH

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.

4.589 × 10⁹⁶(97-digit number)

45892317625075445379…98118129557457505279

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

4.589 × 10⁹⁶(97-digit number)

45892317625075445379…98118129557457505279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.589 × 10⁹⁶(97-digit number)

45892317625075445379…98118129557457505281

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

9.178 × 10⁹⁶(97-digit number)

91784635250150890759…96236259114915010559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.178 × 10⁹⁶(97-digit number)

91784635250150890759…96236259114915010561

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

1.835 × 10⁹⁷(98-digit number)

18356927050030178151…92472518229830021119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.835 × 10⁹⁷(98-digit number)

18356927050030178151…92472518229830021121

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

3.671 × 10⁹⁷(98-digit number)

36713854100060356303…84945036459660042239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.671 × 10⁹⁷(98-digit number)

36713854100060356303…84945036459660042241

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

7.342 × 10⁹⁷(98-digit number)

73427708200120712607…69890072919320084479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.342 × 10⁹⁷(98-digit number)

73427708200120712607…69890072919320084481

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 #430,524

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