Block #443,626

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/14/2014, 4:27:32 PM · Difficulty 10.3477 · 6,364,455 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

caa48441e59201d9ca4814fcff93a73951943888cd0dfee231142d7ffdffa81a

View on Chainz ↗

Height

#443,626

Difficulty

10.347660

Transactions

Size

868 B

Version

Bits

0a590046

Nonce

110,171

Timestamp

3/14/2014, 4:27:32 PM

Confirmations

6,364,455

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

39e80ef3ec9475abf4983b32f3529d1c20236c646b493ed8af41ec3b04ba1e6d

Transactions (1)

Coinbase39e80ef3ec9475…41ec3b04ba1e6d

1 in → 21 out9.3200 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg Adbb4svj…dQWTHsq5 AZr7Ptuw…CM4Yw5jq

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.

8.906 × 10⁹⁶(97-digit number)

89064446091238812329…95955145492711046399

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

8.906 × 10⁹⁶(97-digit number)

89064446091238812329…95955145492711046399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.906 × 10⁹⁶(97-digit number)

89064446091238812329…95955145492711046401

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

1.781 × 10⁹⁷(98-digit number)

17812889218247762465…91910290985422092799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.781 × 10⁹⁷(98-digit number)

17812889218247762465…91910290985422092801

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

3.562 × 10⁹⁷(98-digit number)

35625778436495524931…83820581970844185599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.562 × 10⁹⁷(98-digit number)

35625778436495524931…83820581970844185601

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

7.125 × 10⁹⁷(98-digit number)

71251556872991049863…67641163941688371199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.125 × 10⁹⁷(98-digit number)

71251556872991049863…67641163941688371201

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

1.425 × 10⁹⁸(99-digit number)

14250311374598209972…35282327883376742399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.425 × 10⁹⁸(99-digit number)

14250311374598209972…35282327883376742401

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 #443,626

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