Block #425,871

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 5:53:57 AM · Difficulty 10.3571 · 6,370,433 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76b7ba24eed33b3751efc44d0fa2ae1ee36c58a4368014059ce153ead9f8fa9f

View on Chainz ↗

Height

#425,871

Difficulty

10.357094

Transactions

Size

901 B

Version

Bits

0a5b6a85

Nonce

331,569

Timestamp

3/2/2014, 5:53:57 AM

Confirmations

6,370,433

Mined by

⛏️ aS7dALqxX1WA4yGGdvvcw46Ggu5ZRhhsKjbnXn

Merkle Root

9747db1352afe99e9e92ea3a4a357061cdde5c0cba82500c189df1e27b89be02

Transactions (1)

Coinbase9747db1352afe9…9df1e27b89be02

1 in → 22 out9.3100 XPM811 B

ALqxX1WA…hsKjbnXn AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AXmS7tZu…11YypHLP

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.

2.048 × 10⁹⁴(95-digit number)

20483345916186680628…64910499982495682559

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

2.048 × 10⁹⁴(95-digit number)

20483345916186680628…64910499982495682559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.048 × 10⁹⁴(95-digit number)

20483345916186680628…64910499982495682561

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

4.096 × 10⁹⁴(95-digit number)

40966691832373361256…29820999964991365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.096 × 10⁹⁴(95-digit number)

40966691832373361256…29820999964991365121

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

8.193 × 10⁹⁴(95-digit number)

81933383664746722512…59641999929982730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.193 × 10⁹⁴(95-digit number)

81933383664746722512…59641999929982730241

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

1.638 × 10⁹⁵(96-digit number)

16386676732949344502…19283999859965460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.638 × 10⁹⁵(96-digit number)

16386676732949344502…19283999859965460481

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

3.277 × 10⁹⁵(96-digit number)

32773353465898689004…38567999719930920959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.277 × 10⁹⁵(96-digit number)

32773353465898689004…38567999719930920961

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