Block #425,739

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 3:36:02 AM · Difficulty 10.3578 · 6,370,045 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e77799933e8a9535f10552d370647fdbed4b2d6d71798c0231d39e2db03535c4

View on Chainz ↗

Height

#425,739

Difficulty

10.357795

Transactions

Size

2.31 KB

Version

Bits

0a5b986c

Nonce

30,243

Timestamp

3/2/2014, 3:36:02 AM

Confirmations

6,370,045

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

163b63d118d9777789a92a262fe57fa95e56de6712b5dff9373632bba0de2074

Transactions (3)

Coinbase2f44b72870c9a7…9e90a0c0ff1d86

1 in → 22 out9.3400 XPM811 B

AdFLJFhb…bsaVkAyh AcuM7XiJ…5uND8Jce AZqjMFvv…G8aw2zC8 AVRMvm7T…6PC6keBx ATp4jJhs…TbSgR8Qb

3e1c64398d3ad1…fab6960593c6c2

6 in → 16 out55.6700 XPM1.21 KB

AVCup41c…qE5u23GJ ARrEVN6m…zWjT6LC4 AZgFHRrY…aQ2pD31y AJqSCMbE…ELzwpPmc AJTZmWMz…K4xGSLcs

dad647064ee2b2…5b387489ed6299

1 in → 2 out8.1886 XPM226 B

Aa7yJdtx…roF1vrRx ASByBKdc…MNvZuU7V

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.

9.387 × 10⁹⁶(97-digit number)

93876980916673430218…57729227678549350399

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

9.387 × 10⁹⁶(97-digit number)

93876980916673430218…57729227678549350399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.387 × 10⁹⁶(97-digit number)

93876980916673430218…57729227678549350401

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

1.877 × 10⁹⁷(98-digit number)

18775396183334686043…15458455357098700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.877 × 10⁹⁷(98-digit number)

18775396183334686043…15458455357098700801

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

3.755 × 10⁹⁷(98-digit number)

37550792366669372087…30916910714197401599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.755 × 10⁹⁷(98-digit number)

37550792366669372087…30916910714197401601

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

7.510 × 10⁹⁷(98-digit number)

75101584733338744175…61833821428394803199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.510 × 10⁹⁷(98-digit number)

75101584733338744175…61833821428394803201

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

1.502 × 10⁹⁸(99-digit number)

15020316946667748835…23667642856789606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.502 × 10⁹⁸(99-digit number)

15020316946667748835…23667642856789606401

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