Block #444,948

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 2:01:42 PM · Difficulty 10.3525 · 6,381,485 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ac0d5fa29ef9e291928c4c51b6c79de242d7096b0a3c8015031334ea143b17cf

View on Chainz ↗

Height

#444,948

Difficulty

10.352461

Transactions

Size

901 B

Version

Bits

0a5a3ae7

Nonce

201,609

Timestamp

3/15/2014, 2:01:42 PM

Confirmations

6,381,485

Mined by

⛏️ aS$\AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f78e6ba62143fd7c2a81ceeed2df5b2323517317070218968109e3d62d22fba0

Transactions (1)

Coinbasef78e6ba62143fd…09e3d62d22fba0

1 in → 22 out9.3200 XPM810 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

1.342 × 10⁹⁸(99-digit number)

13429516451605730221…00520791851866951319

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

1.342 × 10⁹⁸(99-digit number)

13429516451605730221…00520791851866951319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.342 × 10⁹⁸(99-digit number)

13429516451605730221…00520791851866951321

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

2.685 × 10⁹⁸(99-digit number)

26859032903211460442…01041583703733902639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.685 × 10⁹⁸(99-digit number)

26859032903211460442…01041583703733902641

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

5.371 × 10⁹⁸(99-digit number)

53718065806422920884…02083167407467805279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.371 × 10⁹⁸(99-digit number)

53718065806422920884…02083167407467805281

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

1.074 × 10⁹⁹(100-digit number)

10743613161284584176…04166334814935610559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.074 × 10⁹⁹(100-digit number)

10743613161284584176…04166334814935610561

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

2.148 × 10⁹⁹(100-digit number)

21487226322569168353…08332669629871221119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.148 × 10⁹⁹(100-digit number)

21487226322569168353…08332669629871221121

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

Block #444,948

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