Block #385,142

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/1/2014, 2:19:49 PM · Difficulty 10.4043 · 6,421,675 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4309d5dfff5d953e0e3635e9d1bd995c6358176991cd7d1febaa17ae004766d9

View on Chainz ↗

Height

#385,142

Difficulty

10.404254

Transactions

Size

434 B

Version

Bits

0a677d2f

Nonce

7,430

Timestamp

2/1/2014, 2:19:49 PM

Confirmations

6,421,675

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

150dec2d7184a371fca6430f06bfa6ee9f37b3ca223790bf06f9bd65b7b6538f

Transactions (2)

Coinbase7b342e2d8acf3e…cb554ef9af5fc3

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

e7de25092aa013…c061c0a9cbf2f7

1 in → 2 out4.1304 XPM227 B

ALQx59LV…R8LoHHSH AYUeGoV2…fdonPhmd

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.

2.521 × 10⁹⁷(98-digit number)

25217368423050658552…44008950314798345479

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

2.521 × 10⁹⁷(98-digit number)

25217368423050658552…44008950314798345479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.521 × 10⁹⁷(98-digit number)

25217368423050658552…44008950314798345481

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

5.043 × 10⁹⁷(98-digit number)

50434736846101317105…88017900629596690959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.043 × 10⁹⁷(98-digit number)

50434736846101317105…88017900629596690961

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

1.008 × 10⁹⁸(99-digit number)

10086947369220263421…76035801259193381919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.008 × 10⁹⁸(99-digit number)

10086947369220263421…76035801259193381921

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

2.017 × 10⁹⁸(99-digit number)

20173894738440526842…52071602518386763839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.017 × 10⁹⁸(99-digit number)

20173894738440526842…52071602518386763841

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

4.034 × 10⁹⁸(99-digit number)

40347789476881053684…04143205036773527679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.034 × 10⁹⁸(99-digit number)

40347789476881053684…04143205036773527681

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 #385,142

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