Block #373,426

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/24/2014, 7:30:04 AM · Difficulty 10.4254 · 6,425,883 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94fe1a970532efdbd30f20a830d32e36c7244268ecd9857e96cde35e2e8d4372

View on Chainz ↗

Height

#373,426

Difficulty

10.425426

Transactions

Size

1.57 KB

Version

Bits

0a6ce8bc

Nonce

59,457

Timestamp

1/24/2014, 7:30:04 AM

Confirmations

6,425,883

Mined by

⛏️ aR4AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

076e9c5d24d64a78b643aaf1654a03103e72e118a6d25295d7b46d5faa37d9ea

Transactions (4)

Coinbasecce3bc1facb019…6c5afc252c6a21

1 in → 23 out9.1900 XPM845 B

AQvZBsUo…hppgRZTJ AXRun4Jx…ReRaSdaU Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AGKhfQo2…h7fBXLX6

86e5c2062a69be…7d81b0e06e2757

1 in → 2 out6.0587 XPM226 B

AZFdfEo8…fU4m2VH6 AP5DvyuR…Q7eyA6Yp

5ab892fe5e732a…3bc7230e32861b

1 in → 2 out2.0705 XPM225 B

AdtoVwp1…nif1KEMS AR7BsVgY…cBPcAhhF

a2cd75fb89cb44…2a3bc3b78041b3

1 in → 2 out4.9793 XPM227 B

APCnYbjA…qhGdy8YN AKJZGvLQ…Qn9KzMD1

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.

7.693 × 10⁹¹(92-digit number)

76934812362564145017…92530447852818617919

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

7.693 × 10⁹¹(92-digit number)

76934812362564145017…92530447852818617919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.693 × 10⁹¹(92-digit number)

76934812362564145017…92530447852818617921

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

1.538 × 10⁹²(93-digit number)

15386962472512829003…85060895705637235839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.538 × 10⁹²(93-digit number)

15386962472512829003…85060895705637235841

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

3.077 × 10⁹²(93-digit number)

30773924945025658006…70121791411274471679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.077 × 10⁹²(93-digit number)

30773924945025658006…70121791411274471681

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

6.154 × 10⁹²(93-digit number)

61547849890051316013…40243582822548943359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.154 × 10⁹²(93-digit number)

61547849890051316013…40243582822548943361

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

1.230 × 10⁹³(94-digit number)

12309569978010263202…80487165645097886719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.230 × 10⁹³(94-digit number)

12309569978010263202…80487165645097886721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.461 × 10⁹³(94-digit number)

24619139956020526405…60974331290195773439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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