Block #440,148

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 5:36:58 AM · Difficulty 10.3519 · 6,350,792 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

66d637e26439a12d7467c299c5fff81b31d476ebbb249452585f3e62ab790299

View on Chainz ↗

Height

#440,148

Difficulty

10.351881

Transactions

Size

9.16 KB

Version

Bits

0a5a14e1

Nonce

110,146

Timestamp

3/12/2014, 5:36:58 AM

Confirmations

6,350,792

Merkle Root

9509e344b96eb28aa9f3c2ef42ff89bd62eefc6f19c0bc015f8c2154ea691b84

Transactions (3)

Coinbasea616bfb625ff40…73f0d991910b19

1 in → 1 out9.4300 XPM101 B

ASXb8Msj…BxGf64iZ

7258b68edc5231…cc4925ba50de36

27 in → 2 out15.1400 XPM3.98 KB

AHGjT5FG…7ApbeqmU AYXmvsdN…7XpW51Gd

dd09a287f31df4…a19570f461fcb4

34 in → 2 out19.0771 XPM4.99 KB

AFucqHWN…CdcU3h8w AHGjT5FG…7ApbeqmU

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.

1.459 × 10⁹²(93-digit number)

14599307227397545050…78295052555087859359

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

1.459 × 10⁹²(93-digit number)

14599307227397545050…78295052555087859359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.459 × 10⁹²(93-digit number)

14599307227397545050…78295052555087859361

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

2.919 × 10⁹²(93-digit number)

29198614454795090101…56590105110175718719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.919 × 10⁹²(93-digit number)

29198614454795090101…56590105110175718721

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

5.839 × 10⁹²(93-digit number)

58397228909590180202…13180210220351437439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.839 × 10⁹²(93-digit number)

58397228909590180202…13180210220351437441

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

1.167 × 10⁹³(94-digit number)

11679445781918036040…26360420440702874879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.167 × 10⁹³(94-digit number)

11679445781918036040…26360420440702874881

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

2.335 × 10⁹³(94-digit number)

23358891563836072080…52720840881405749759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.335 × 10⁹³(94-digit number)

23358891563836072080…52720840881405749761

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