Block #427,746

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 2:07:14 PM · Difficulty 10.3512 · 6,399,265 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

da171ca5164890bb42da210beaa62621b9d63817378e0104af68ddb8d176184a

View on Chainz ↗

Height

#427,746

Difficulty

10.351247

Transactions

Size

541 B

Version

Bits

0a59eb5b

Nonce

124,512

Timestamp

3/3/2014, 2:07:14 PM

Confirmations

6,399,265

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

370d0391176f5f06532aab3ed8f03b15f5d55545c86e915a5e488874623e5e18

Transactions (2)

Coinbase4723fce9912d7f…a305bfee9749d1

1 in → 1 out9.3300 XPM110 B

AeKNrjNj…1NEq95Ta

105fc21fe31c1b…57b70aa1a03e3e

2 in → 1 out3.1917 XPM340 B

AGKj1VZw…bhwpBHGN

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.

1.248 × 10⁹⁸(99-digit number)

12487642262139467038…82857092679757173599

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

1.248 × 10⁹⁸(99-digit number)

12487642262139467038…82857092679757173599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.248 × 10⁹⁸(99-digit number)

12487642262139467038…82857092679757173601

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

2.497 × 10⁹⁸(99-digit number)

24975284524278934077…65714185359514347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.497 × 10⁹⁸(99-digit number)

24975284524278934077…65714185359514347201

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

4.995 × 10⁹⁸(99-digit number)

49950569048557868155…31428370719028694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.995 × 10⁹⁸(99-digit number)

49950569048557868155…31428370719028694401

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

9.990 × 10⁹⁸(99-digit number)

99901138097115736311…62856741438057388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.990 × 10⁹⁸(99-digit number)

99901138097115736311…62856741438057388801

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

1.998 × 10⁹⁹(100-digit number)

19980227619423147262…25713482876114777599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.998 × 10⁹⁹(100-digit number)

19980227619423147262…25713482876114777601

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 #427,746

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