Block #334,001

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 4:48:25 AM · Difficulty 10.1592 · 6,478,537 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

40667d4e7e235aaa735f53ccf37ca752711398f974fa191927cbc79549eb4c0c

View on Chainz ↗

Height

#334,001

Difficulty

10.159192

Transactions

Size

1.39 KB

Version

Bits

0a28c0d2

Nonce

1,578

Timestamp

12/29/2013, 4:48:25 AM

Confirmations

6,478,537

Mined by

⛏️ aRAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

7769f564a54ec6c0adf348c6712836e228041f4031a0c304bf5d6209dafe9fb6

Transactions (2)

Coinbase9d1dbe15c41ea5…6154dd73c6b0d1

1 in → 22 out9.6700 XPM811 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AXeQnyEs…fUWKQwq8

1478e9c023b857…82731136de55e8

3 in → 2 out1010.3044 XPM522 B

AWhxzjMi…aSBRDi4y AcQwzWoM…Wbj4NQTR

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.

2.565 × 10⁹⁴(95-digit number)

25653091097989206209…59860467051264282399

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

2.565 × 10⁹⁴(95-digit number)

25653091097989206209…59860467051264282399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.565 × 10⁹⁴(95-digit number)

25653091097989206209…59860467051264282401

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

5.130 × 10⁹⁴(95-digit number)

51306182195978412418…19720934102528564799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.130 × 10⁹⁴(95-digit number)

51306182195978412418…19720934102528564801

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

1.026 × 10⁹⁵(96-digit number)

10261236439195682483…39441868205057129599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.026 × 10⁹⁵(96-digit number)

10261236439195682483…39441868205057129601

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

2.052 × 10⁹⁵(96-digit number)

20522472878391364967…78883736410114259199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.052 × 10⁹⁵(96-digit number)

20522472878391364967…78883736410114259201

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

4.104 × 10⁹⁵(96-digit number)

41044945756782729934…57767472820228518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.104 × 10⁹⁵(96-digit number)

41044945756782729934…57767472820228518401

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 #334,001

Cookie Preferences