Block #271,818

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 8:42:09 PM · Difficulty 9.9525 · 6,532,387 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e686d069807d509311b2e776e6cb9d358c83d3c7f5d78b6b5d97b0c1a04f5f3

View on Chainz ↗

Height

#271,818

Difficulty

9.952459

Transactions

Size

1.14 KB

Version

Bits

09f3d459

Nonce

22,219

Timestamp

11/24/2013, 8:42:09 PM

Confirmations

6,532,387

Mined by

⛏️ P2SHAGEV5fApubMy3SpfHCfNwHy5rktNgEsm1s

Merkle Root

d24bff16cd0a756f6b097638d3e7fa105ff4747445d8d48658dde936caf26db2

Transactions (2)

Coinbasef1a8b6e3c4a673…8f0590c6f5c91f

1 in → 1 out10.0900 XPM109 B

AGEV5fAp…tNgEsm1s

a81cf4751adf7e…70f18477f4d618

6 in → 2 out180.0104 XPM963 B

ATJi3RtC…sSxGmpuT AX8sCRi6…LbhCGS2k

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.

2.157 × 10⁹⁷(98-digit number)

21579518056934509805…89102436611768442639

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

2.157 × 10⁹⁷(98-digit number)

21579518056934509805…89102436611768442639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.157 × 10⁹⁷(98-digit number)

21579518056934509805…89102436611768442641

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

4.315 × 10⁹⁷(98-digit number)

43159036113869019610…78204873223536885279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.315 × 10⁹⁷(98-digit number)

43159036113869019610…78204873223536885281

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

8.631 × 10⁹⁷(98-digit number)

86318072227738039221…56409746447073770559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.631 × 10⁹⁷(98-digit number)

86318072227738039221…56409746447073770561

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

1.726 × 10⁹⁸(99-digit number)

17263614445547607844…12819492894147541119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.726 × 10⁹⁸(99-digit number)

17263614445547607844…12819492894147541121

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

3.452 × 10⁹⁸(99-digit number)

34527228891095215688…25638985788295082239

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