Block #271,485

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 4:08:08 PM · Difficulty 9.9519 · 6,532,539 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9210b8fb7928483c3a9624a9bb5d5dfd5302abd00bffa2b66b8ababc3c25e0e

View on Chainz ↗

Height

#271,485

Difficulty

9.951897

Transactions

Size

424 B

Version

Bits

09f3af89

Nonce

30,264

Timestamp

11/24/2013, 4:08:08 PM

Confirmations

6,532,539

Mined by

⛏️ P2SHANWrHiAp1jAKM5aGHVgFxnabiNY2WAv4pT

Merkle Root

8bc1dde0888c0fab24fc104863f77553ee2c5a8513262c9f1f70c83b5ddd4e51

Transactions (2)

Coinbase714b69e39c9c2f…a5a6fc0e9d1e26

1 in → 1 out10.0900 XPM109 B

ANWrHiAp…Y2WAv4pT

2a7b7c4e6b919b…3b26e73d84d15c

1 in → 2 out6.0254 XPM226 B

Aa8YsoAD…FZGEemxV AaVFHFSq…bCnX1Bpw

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.

1.220 × 10⁹²(93-digit number)

12205884714398667159…79794111169752781279

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

1.220 × 10⁹²(93-digit number)

12205884714398667159…79794111169752781279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.220 × 10⁹²(93-digit number)

12205884714398667159…79794111169752781281

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

2.441 × 10⁹²(93-digit number)

24411769428797334319…59588222339505562559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.441 × 10⁹²(93-digit number)

24411769428797334319…59588222339505562561

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

4.882 × 10⁹²(93-digit number)

48823538857594668639…19176444679011125119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.882 × 10⁹²(93-digit number)

48823538857594668639…19176444679011125121

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

9.764 × 10⁹²(93-digit number)

97647077715189337279…38352889358022250239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.764 × 10⁹²(93-digit number)

97647077715189337279…38352889358022250241

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

1.952 × 10⁹³(94-digit number)

19529415543037867455…76705778716044500479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.952 × 10⁹³(94-digit number)

19529415543037867455…76705778716044500481

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