Block #227,248

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/25/2013, 6:15:06 PM · Difficulty 9.9366 · 6,570,875 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

014943c2a2bb11183eb583a0cfea76a68aead55d5765dc1a1333ae683d614528

View on Chainz ↗

Height

#227,248

Difficulty

9.936595

Transactions

Size

424 B

Version

Bits

09efc4b7

Nonce

102,898

Timestamp

10/25/2013, 6:15:06 PM

Confirmations

6,570,875

Mined by

⛏️ P2SHAHPLSWVdVVmfZ1Mw8oxTBdXzN3ZdicvSUu

Merkle Root

11592dfc0716874542d2b9739529da3f3511610bc74a6805022a60c976b8e572

Transactions (2)

Coinbasefb764d9376a6b1…7a67fffd579337

1 in → 1 out10.1200 XPM109 B

AHPLSWVd…ZdicvSUu

35bf2616d41f21…006d9717cf9972

1 in → 2 out8.0029 XPM225 B

Ab7PSehG…aCpbzHQ4 AUfBNY3y…Mm2UYiNj

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.

9.479 × 10⁹³(94-digit number)

94794068066964047324…27622185556712895199

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

9.479 × 10⁹³(94-digit number)

94794068066964047324…27622185556712895199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.479 × 10⁹³(94-digit number)

94794068066964047324…27622185556712895201

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

1.895 × 10⁹⁴(95-digit number)

18958813613392809464…55244371113425790399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.895 × 10⁹⁴(95-digit number)

18958813613392809464…55244371113425790401

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

3.791 × 10⁹⁴(95-digit number)

37917627226785618929…10488742226851580799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.791 × 10⁹⁴(95-digit number)

37917627226785618929…10488742226851580801

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

7.583 × 10⁹⁴(95-digit number)

75835254453571237859…20977484453703161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.583 × 10⁹⁴(95-digit number)

75835254453571237859…20977484453703161601

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

1.516 × 10⁹⁵(96-digit number)

15167050890714247571…41954968907406323199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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