Block #444,995

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/15/2014, 2:52:10 PM · Difficulty 10.3521 · 6,365,187 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0ddd31e0afcfca98211de395ae0fa65d06e0378c215b3e9fc9e57626a81751b

View on Chainz ↗

Height

#444,995

Difficulty

10.352072

Transactions

Size

1.13 KB

Version

Bits

0a5a2164

Nonce

145,958

Timestamp

3/15/2014, 2:52:10 PM

Confirmations

6,365,187

Mined by

⛏️ CaS$hAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c5edc2763301299114d92df4338edf0ba7d9a6e9648ad7f6492307997ac35f3d

Transactions (2)

Coinbaseabdee2224799b6…e623348307187a

1 in → 23 out9.3200 XPM845 B

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

b0e266298c72f2…41a21c6d725d6c

1 in → 2 out2.1792 XPM226 B

AWxdQRRv…5tony3zU AWaxTsag…PL1cyPDP

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.

9.663 × 10⁹⁶(97-digit number)

96633305636572893831…21451938853688099159

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

9.663 × 10⁹⁶(97-digit number)

96633305636572893831…21451938853688099159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.663 × 10⁹⁶(97-digit number)

96633305636572893831…21451938853688099161

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

1.932 × 10⁹⁷(98-digit number)

19326661127314578766…42903877707376198319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.932 × 10⁹⁷(98-digit number)

19326661127314578766…42903877707376198321

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

3.865 × 10⁹⁷(98-digit number)

38653322254629157532…85807755414752396639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.865 × 10⁹⁷(98-digit number)

38653322254629157532…85807755414752396641

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

7.730 × 10⁹⁷(98-digit number)

77306644509258315065…71615510829504793279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.730 × 10⁹⁷(98-digit number)

77306644509258315065…71615510829504793281

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

1.546 × 10⁹⁸(99-digit number)

15461328901851663013…43231021659009586559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.546 × 10⁹⁸(99-digit number)

15461328901851663013…43231021659009586561

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 #444,995

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