Block #341,518

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/3/2014, 12:20:17 PM · Difficulty 10.1392 · 6,459,101 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ef44f214aba1d0f58bca3fa0f5ac73094b7814dbfccffe7b9db82774da2bbaa

View on Chainz ↗

Height

#341,518

Difficulty

10.139240

Transactions

Size

901 B

Version

Bits

0a23a538

Nonce

1,417

Timestamp

1/3/2014, 12:20:17 PM

Confirmations

6,459,101

Mined by

⛏️ 6aRAayReikY2pZFemmazWEAhY9ZS62HAC42fs

Merkle Root

07d0190e6bf8551b44c476e46de46447c0f0bb9805b4c7057262e8e430112e00

Transactions (1)

Coinbase07d0190e6bf855…62e8e430112e00

1 in → 22 out9.7100 XPM811 B

AayReikY…2HAC42fs ANKaTXA5…XnCS2N8b AG5YAjec…VhA4Aeh1 AQGCHb82…JSz7xv5Z AXeQnyEs…fUWKQwq8

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.

8.714 × 10⁹⁴(95-digit number)

87143809846263344764…52909590410078988799

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

8.714 × 10⁹⁴(95-digit number)

87143809846263344764…52909590410078988799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.714 × 10⁹⁴(95-digit number)

87143809846263344764…52909590410078988801

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

1.742 × 10⁹⁵(96-digit number)

17428761969252668952…05819180820157977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.742 × 10⁹⁵(96-digit number)

17428761969252668952…05819180820157977601

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

3.485 × 10⁹⁵(96-digit number)

34857523938505337905…11638361640315955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.485 × 10⁹⁵(96-digit number)

34857523938505337905…11638361640315955201

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

6.971 × 10⁹⁵(96-digit number)

69715047877010675811…23276723280631910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.971 × 10⁹⁵(96-digit number)

69715047877010675811…23276723280631910401

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

1.394 × 10⁹⁶(97-digit number)

13943009575402135162…46553446561263820799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.394 × 10⁹⁶(97-digit number)

13943009575402135162…46553446561263820801

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