Block #294,271

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/4/2013, 7:07:12 PM · Difficulty 9.9909 · 6,523,663 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f780283e21579543b51b11df38959e811941fe5c8a96090599b01ed963094dfd

View on Chainz ↗

Height

#294,271

Difficulty

9.990942

Transactions

Size

934 B

Version

Bits

09fdae67

Nonce

14,974

Timestamp

12/4/2013, 7:07:12 PM

Confirmations

6,523,663

Mined by

⛏️ }aR}bAVaz6eMXHfWpEaykk35REAtp3FTCAgqi1U

Merkle Root

f9fb727b1749adb3a99ec233540c77cd8b4847c0bee5ed421d86b8ac8cba3b6f

Transactions (1)

Coinbasef9fb727b1749ad…86b8ac8cba3b6f

1 in → 23 out10.0000 XPM845 B

AVaz6eMX…TCAgqi1U AWuQdP8q…6YMDw92f AcaLouCs…xPDq8Sis AGXewNDY…FgKQN3gK ALGUvc8x…qDYGNLfB

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.

3.448 × 10⁹³(94-digit number)

34483744350241616114…62206285581854108159

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

3.448 × 10⁹³(94-digit number)

34483744350241616114…62206285581854108159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.448 × 10⁹³(94-digit number)

34483744350241616114…62206285581854108161

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

6.896 × 10⁹³(94-digit number)

68967488700483232229…24412571163708216319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.896 × 10⁹³(94-digit number)

68967488700483232229…24412571163708216321

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

1.379 × 10⁹⁴(95-digit number)

13793497740096646445…48825142327416432639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.379 × 10⁹⁴(95-digit number)

13793497740096646445…48825142327416432641

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

2.758 × 10⁹⁴(95-digit number)

27586995480193292891…97650284654832865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.758 × 10⁹⁴(95-digit number)

27586995480193292891…97650284654832865281

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

5.517 × 10⁹⁴(95-digit number)

55173990960386585783…95300569309665730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.517 × 10⁹⁴(95-digit number)

55173990960386585783…95300569309665730561

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 #294,271

Cookie Preferences