Block #445,337

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 8:08:53 PM · Difficulty 10.3553 · 6,360,731 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1514abe898c065264de7336315c880f6d25915c8abd2c3d7c9e332ce28352f47

View on Chainz ↗

Height

#445,337

Difficulty

10.355278

Transactions

Size

1.54 KB

Version

Bits

0a5af383

Nonce

140,363

Timestamp

3/15/2014, 8:08:53 PM

Confirmations

6,360,731

Mined by

⛏️ aS$AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

5b19e39d13b7794bbeaac975852bbc8e959e46bee4be4431ba1dafedca2608b1

Transactions (4)

Coinbasea1f3041dde5e7b…513968b1260eaf

1 in → 22 out9.3100 XPM811 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn ARSeozDw…C9HtARnj

29d9c7cf5e6c1b…c9a68c964e6c22

1 in → 2 out9.2700 XPM226 B

AGNfqxNt…iRo3jheR AVyicbpv…VbHvXmrQ

3d14c94d4e894d…d20bc2a9ee0ab3

1 in → 2 out9.2700 XPM226 B

AUj89Lsc…nyDgyc6f AGs28gMH…22psHe5N

89dacb7a058aee…76507d4d5ab2e0

1 in → 2 out9.2700 XPM226 B

AKj3jLpD…urBSDLtG Ab7KvdoN…BMF3E7hn

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.

6.938 × 10⁹⁸(99-digit number)

69387371027745996867…96359904374963077119

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

6.938 × 10⁹⁸(99-digit number)

69387371027745996867…96359904374963077119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.938 × 10⁹⁸(99-digit number)

69387371027745996867…96359904374963077121

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

1.387 × 10⁹⁹(100-digit number)

13877474205549199373…92719808749926154239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.387 × 10⁹⁹(100-digit number)

13877474205549199373…92719808749926154241

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

2.775 × 10⁹⁹(100-digit number)

27754948411098398746…85439617499852308479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.775 × 10⁹⁹(100-digit number)

27754948411098398746…85439617499852308481

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

5.550 × 10⁹⁹(100-digit number)

55509896822196797493…70879234999704616959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.550 × 10⁹⁹(100-digit number)

55509896822196797493…70879234999704616961

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

1.110 × 10¹⁰⁰(101-digit number)

11101979364439359498…41758469999409233919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.110 × 10¹⁰⁰(101-digit number)

11101979364439359498…41758469999409233921

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