Block #436,946

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 10:54:36 PM · Difficulty 10.3596 · 6,371,089 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

77c7fcbcee2855baa5c641138203cf232703ba29ec6694b113004830dcfb3e14

View on Chainz ↗

Height

#436,946

Difficulty

10.359610

Transactions

Size

1004 B

Version

Bits

0a5c0f5f

Nonce

141,506

Timestamp

3/9/2014, 10:54:36 PM

Confirmations

6,371,089

Mined by

⛏️ aS|ANNg88pGRQwFs2RfTXspDobTEJppn21sTe

Merkle Root

f31749d199dd790903b42590f98917980ba0a4c6565d63002df6206a5cf8e66e

Transactions (1)

Coinbasef31749d199dd79…f6206a5cf8e66e

1 in → 25 out9.3000 XPM913 B

ANNg88pG…ppn21sTe Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

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.

1.102 × 10⁹⁷(98-digit number)

11023426652868539008…67785666826844420659

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

1.102 × 10⁹⁷(98-digit number)

11023426652868539008…67785666826844420659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.102 × 10⁹⁷(98-digit number)

11023426652868539008…67785666826844420661

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

2.204 × 10⁹⁷(98-digit number)

22046853305737078017…35571333653688841319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.204 × 10⁹⁷(98-digit number)

22046853305737078017…35571333653688841321

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

4.409 × 10⁹⁷(98-digit number)

44093706611474156035…71142667307377682639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.409 × 10⁹⁷(98-digit number)

44093706611474156035…71142667307377682641

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

8.818 × 10⁹⁷(98-digit number)

88187413222948312071…42285334614755365279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.818 × 10⁹⁷(98-digit number)

88187413222948312071…42285334614755365281

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

1.763 × 10⁹⁸(99-digit number)

17637482644589662414…84570669229510730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.763 × 10⁹⁸(99-digit number)

17637482644589662414…84570669229510730561

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 #436,946

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