Block #373,601

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 10:30:56 AM · Difficulty 10.4248 · 6,425,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

117b2f77bf56099621cb2347f031940e77a8d8f7f92c9f0370642f69a90b6dea

View on Chainz ↗

Height

#373,601

Difficulty

10.424756

Transactions

Size

884 B

Version

Bits

0a6cbcc9

Nonce

73,976

Timestamp

1/24/2014, 10:30:56 AM

Confirmations

6,425,214

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

0ffacfc0f97379f9b6164874e7d9a3f20a4d9e409e136e25750b1c533ceb9e22

Transactions (4)

Coinbase0ee8db489707de…284b3f00f35433

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

c0c57c2d3cf136…da64ac103e2762

1 in → 2 out9.1500 XPM226 B

AZdV5WCw…KuN9geW7 ASjrLALu…uuzn6Z1S

9a15fbdd46e42c…d1903c076e5a0c

1 in → 2 out9.1500 XPM226 B

AMLdK2Nf…FLKpMU8c AbJDWL7j…2X5Yb4qH

8d9b03a5ade125…8b286b867670c1

1 in → 2 out9.1500 XPM225 B

AKQ3RCZC…B3eNConE Ad9TYdsg…yMvCzyu8

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.

4.661 × 10⁹⁷(98-digit number)

46613644397484379645…09643124807607665119

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

4.661 × 10⁹⁷(98-digit number)

46613644397484379645…09643124807607665119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.661 × 10⁹⁷(98-digit number)

46613644397484379645…09643124807607665121

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

9.322 × 10⁹⁷(98-digit number)

93227288794968759291…19286249615215330239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.322 × 10⁹⁷(98-digit number)

93227288794968759291…19286249615215330241

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

1.864 × 10⁹⁸(99-digit number)

18645457758993751858…38572499230430660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.864 × 10⁹⁸(99-digit number)

18645457758993751858…38572499230430660481

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

3.729 × 10⁹⁸(99-digit number)

37290915517987503716…77144998460861320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.729 × 10⁹⁸(99-digit number)

37290915517987503716…77144998460861320961

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

7.458 × 10⁹⁸(99-digit number)

74581831035975007433…54289996921722641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.458 × 10⁹⁸(99-digit number)

74581831035975007433…54289996921722641921

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