Block #242,635

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 8:39:33 PM · Difficulty 9.9602 · 6,560,051 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

959c1e536917eb6f55a76331d8540f84a4c15eb7e34ee10ff788d5e3f648e71a

View on Chainz ↗

Height

#242,635

Difficulty

9.960200

Transactions

Size

1.61 KB

Version

Bits

09f5cfa6

Nonce

144,761

Timestamp

11/3/2013, 8:39:33 PM

Confirmations

6,560,051

Mined by

⛏️ Rv>ANmkKL2U9tSUyN8ojZRwqDzhmbjPxj1Qs3

Merkle Root

42c9578c6cc24436823462ef88737d3109ea07795a3d044d921a59bf7be0f324

Transactions (1)

Coinbase42c9578c6cc244…1a59bf7be0f324

1 in → 44 out10.0400 XPM1.52 KB

ANmkKL2U…jPxj1Qs3 AQtzUSwq…htAuF3yC AKDTDDtx…iqvw9cdY AHkgKuuD…TkWqWiw1 ANo4YY1x…vnsPRDSU

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.

1.093 × 10⁹³(94-digit number)

10938520866714645811…83600673393813784319

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

1.093 × 10⁹³(94-digit number)

10938520866714645811…83600673393813784319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.093 × 10⁹³(94-digit number)

10938520866714645811…83600673393813784321

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

2.187 × 10⁹³(94-digit number)

21877041733429291623…67201346787627568639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.187 × 10⁹³(94-digit number)

21877041733429291623…67201346787627568641

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

4.375 × 10⁹³(94-digit number)

43754083466858583247…34402693575255137279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.375 × 10⁹³(94-digit number)

43754083466858583247…34402693575255137281

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

8.750 × 10⁹³(94-digit number)

87508166933717166494…68805387150510274559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.750 × 10⁹³(94-digit number)

87508166933717166494…68805387150510274561

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

1.750 × 10⁹⁴(95-digit number)

17501633386743433298…37610774301020549119

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