Block #435,426

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2014, 10:10:25 PM · Difficulty 10.3553 · 6,360,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5553820dc908d24df9faf4a6315529bb07cde8fc3f95307cb89e6e9d9f8941e0

View on Chainz ↗

Height

#435,426

Difficulty

10.355261

Transactions

Size

20.05 KB

Version

Bits

0a5af268

Nonce

108,543

Timestamp

3/8/2014, 10:10:25 PM

Confirmations

6,360,637

Mined by

⛏️ aSbAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

e5f90bd73f73779f98939e1ddeecf39a489b90d96a476db3e5fd4c47403e5514

Transactions (4)

Coinbase249ba73edf5b85…a164c692318b82

1 in → 25 out9.3100 XPM913 B

AQvZBsUo…hppgRZTJ AGD4yZQw…hGzM2XAx Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

452809a7e94e4f…c25d8cbe6d22aa

4 in → 12 out37.3300 XPM873 B

AGMJA6YS…H8zUpSxi ATAxh43K…62WhpjvU AMeyeZ9L…gJoDemgf ANt8CsTm…XxNi34u4 AdKrkQzd…yvN4n1W8

0619b7aee4c726…c835937c846f37

43 in → 2 out128.3616 XPM6.29 KB

ARbmkaHd…Dz7PvdqY AXpHj8VG…p14M3hZe

d826b789776fbe…ce5ccbf4821745

82 in → 2 out32.0887 XPM11.93 KB

Ae15418y…NN5bVKkm AJpHPZ1t…U3J2eZCz

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.

3.962 × 10⁹¹(92-digit number)

39623194823617056741…52020393809990875799

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

3.962 × 10⁹¹(92-digit number)

39623194823617056741…52020393809990875799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.962 × 10⁹¹(92-digit number)

39623194823617056741…52020393809990875801

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

7.924 × 10⁹¹(92-digit number)

79246389647234113483…04040787619981751599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.924 × 10⁹¹(92-digit number)

79246389647234113483…04040787619981751601

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

1.584 × 10⁹²(93-digit number)

15849277929446822696…08081575239963503199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.584 × 10⁹²(93-digit number)

15849277929446822696…08081575239963503201

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

3.169 × 10⁹²(93-digit number)

31698555858893645393…16163150479927006399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.169 × 10⁹²(93-digit number)

31698555858893645393…16163150479927006401

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

6.339 × 10⁹²(93-digit number)

63397111717787290786…32326300959854012799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.339 × 10⁹²(93-digit number)

63397111717787290786…32326300959854012801

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