Block #439,656

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 8:20:44 PM · Difficulty 10.3604 · 6,369,456 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fe8a1369c2707fda3eef9111334905d9d195a8a018075d3d36aa4f8616aa49e

View on Chainz ↗

Height

#439,656

Difficulty

10.360416

Transactions

Size

968 B

Version

Bits

0a5c4435

Nonce

457,868

Timestamp

3/11/2014, 8:20:44 PM

Confirmations

6,369,456

Mined by

⛏️ haSoVAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

cce1e996153192295d7ad6704136142bb6cfbd8b76cc9b99b005aa00c3872f1e

Transactions (1)

Coinbasecce1e996153192…05aa00c3872f1e

1 in → 24 out9.3000 XPM879 B

AQvZBsUo…hppgRZTJ 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.

1.291 × 10⁹³(94-digit number)

12912957817296921774…05671433537869606499

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

1.291 × 10⁹³(94-digit number)

12912957817296921774…05671433537869606499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.291 × 10⁹³(94-digit number)

12912957817296921774…05671433537869606501

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

2.582 × 10⁹³(94-digit number)

25825915634593843549…11342867075739212999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.582 × 10⁹³(94-digit number)

25825915634593843549…11342867075739213001

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

5.165 × 10⁹³(94-digit number)

51651831269187687099…22685734151478425999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.165 × 10⁹³(94-digit number)

51651831269187687099…22685734151478426001

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

1.033 × 10⁹⁴(95-digit number)

10330366253837537419…45371468302956851999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.033 × 10⁹⁴(95-digit number)

10330366253837537419…45371468302956852001

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

2.066 × 10⁹⁴(95-digit number)

20660732507675074839…90742936605913703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.066 × 10⁹⁴(95-digit number)

20660732507675074839…90742936605913704001

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 #439,656

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