Block #378,862

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/28/2014, 4:11:45 AM · Difficulty 10.4127 · 6,430,544 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

53b1df480c0ccdda08a550e293c946af6d6c315584b6d83943af451e838e349b

View on Chainz ↗

Height

#378,862

Difficulty

10.412667

Transactions

Size

1.23 KB

Version

Bits

0a69a48b

Nonce

30,910

Timestamp

1/28/2014, 4:11:45 AM

Confirmations

6,430,544

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3c9e74b14eab1ea6ee1bdebed4565c8c23a4c7e5d5bb019baaa8fd5b8bf178fd

Transactions (5)

Coinbase7a943adba76a27…e0659289ae7c8a

1 in → 1 out9.2500 XPM116 B

AbwWkWZt…kawDhufa

d31074680af24e…2c743fc4f72270

1 in → 2 out6.1463 XPM225 B

AP92We7w…NSceBvgq AV7y4PWJ…7EwgdbTY

903e415a952873…b5023b229501f5

1 in → 2 out6.1400 XPM226 B

AZnEvtDp…dYrFbS9Z AJyzWRdQ…FDU6pY1M

0be6887904ef6e…592a0bfbda4319

1 in → 2 out2.0916 XPM226 B

Ac24WwPt…BSeTbxUj AaTMiXzZ…LPpftemh

894fd575a70d0a…9c8c5ad000dc5e

2 in → 2 out5.0688 XPM374 B

ARZ9w5Nr…c8A4keKY AWGkwaNj…bnuHkM1P

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.

4.136 × 10¹⁰⁶(107-digit number)

41361412074379969190…55346473869157601279

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

4.136 × 10¹⁰⁶(107-digit number)

41361412074379969190…55346473869157601279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.136 × 10¹⁰⁶(107-digit number)

41361412074379969190…55346473869157601281

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

8.272 × 10¹⁰⁶(107-digit number)

82722824148759938380…10692947738315202559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.272 × 10¹⁰⁶(107-digit number)

82722824148759938380…10692947738315202561

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

1.654 × 10¹⁰⁷(108-digit number)

16544564829751987676…21385895476630405119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.654 × 10¹⁰⁷(108-digit number)

16544564829751987676…21385895476630405121

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

3.308 × 10¹⁰⁷(108-digit number)

33089129659503975352…42771790953260810239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.308 × 10¹⁰⁷(108-digit number)

33089129659503975352…42771790953260810241

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

6.617 × 10¹⁰⁷(108-digit number)

66178259319007950704…85543581906521620479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.617 × 10¹⁰⁷(108-digit number)

66178259319007950704…85543581906521620481

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 #378,862

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