Block #439,086

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/11/2014, 10:50:36 AM · Difficulty 10.3593 · 6,375,224 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7359f44a758427f8be58a354e57c840834e634065d922955ff7c9e3bae9bbd62

View on Chainz ↗

Height

#439,086

Difficulty

10.359338

Transactions

Size

434 B

Version

Bits

0a5bfd92

Nonce

22,262

Timestamp

3/11/2014, 10:50:36 AM

Confirmations

6,375,224

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

15aa0ee8df7b949d44cde20236aec9b7cae3ad8a8ced3ebe63e7cd64a2328f8b

Transactions (2)

Coinbase9a40e811cd31c5…d177484b876542

1 in → 1 out9.3100 XPM116 B

AbwWkWZt…kawDhufa

ee1c09bcd00165…f09efcdd1ccec4

1 in → 2 out2.6302 XPM226 B

AZUULBDY…cj2g39J3 AZTS3grf…3mKBxi7k

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.

4.276 × 10⁹⁸(99-digit number)

42767225608270217477…35650737629846806239

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

4.276 × 10⁹⁸(99-digit number)

42767225608270217477…35650737629846806239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.276 × 10⁹⁸(99-digit number)

42767225608270217477…35650737629846806241

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

8.553 × 10⁹⁸(99-digit number)

85534451216540434955…71301475259693612479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.553 × 10⁹⁸(99-digit number)

85534451216540434955…71301475259693612481

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

1.710 × 10⁹⁹(100-digit number)

17106890243308086991…42602950519387224959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.710 × 10⁹⁹(100-digit number)

17106890243308086991…42602950519387224961

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

3.421 × 10⁹⁹(100-digit number)

34213780486616173982…85205901038774449919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.421 × 10⁹⁹(100-digit number)

34213780486616173982…85205901038774449921

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

6.842 × 10⁹⁹(100-digit number)

68427560973232347964…70411802077548899839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.842 × 10⁹⁹(100-digit number)

68427560973232347964…70411802077548899841

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 #439,086

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