Block #291,447

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/3/2013, 4:48:11 AM · Difficulty 9.9899 · 6,533,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b8b94e612a04e81078256760c8964821d5bf28858fe503b72d0e00d3a59215e9

View on Chainz ↗

Height

#291,447

Difficulty

9.989855

Transactions

Size

1.08 KB

Version

Bits

09fd6720

Nonce

17,389

Timestamp

12/3/2013, 4:48:11 AM

Confirmations

6,533,409

Mined by

⛏️ wraRbQ6AZninDSu1Gy3NdWkaTGfLDa2i9FvgDMwC4

Merkle Root

884badd4f8e2377abbd99975cda878f4dc61110fc63d97cea1a8935549b60e9e

Transactions (1)

Coinbase884badd4f8e237…a8935549b60e9e

1 in → 28 out9.9900 XPM1015 B

AZninDSu…FvgDMwC4 AYcLTeXR…bscgPops ARXSrG7z…CRW69WR4 AV38iKvB…ThTfXfGh AdyKWr2A…7PSnFqeJ

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.

3.258 × 10⁹⁵(96-digit number)

32589753178949749112…57069470756613676799

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

3.258 × 10⁹⁵(96-digit number)

32589753178949749112…57069470756613676799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.258 × 10⁹⁵(96-digit number)

32589753178949749112…57069470756613676801

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

6.517 × 10⁹⁵(96-digit number)

65179506357899498225…14138941513227353599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.517 × 10⁹⁵(96-digit number)

65179506357899498225…14138941513227353601

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

1.303 × 10⁹⁶(97-digit number)

13035901271579899645…28277883026454707199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.303 × 10⁹⁶(97-digit number)

13035901271579899645…28277883026454707201

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

2.607 × 10⁹⁶(97-digit number)

26071802543159799290…56555766052909414399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.607 × 10⁹⁶(97-digit number)

26071802543159799290…56555766052909414401

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

5.214 × 10⁹⁶(97-digit number)

52143605086319598580…13111532105818828799

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

Block #291,447

Cookie Preferences