Block #271,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 2:39:10 PM · Difficulty 9.9518 · 6,524,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a7c36d9e5cd9c5fc7140fca45ecc0a3a87c3b6d29e71581603d4f45a8a271e75

View on Chainz ↗

Height

#271,386

Difficulty

9.951810

Transactions

Size

1002 B

Version

Bits

09f3a9d8

Nonce

17,952

Timestamp

11/24/2013, 2:39:10 PM

Confirmations

6,524,873

Mined by

⛏️ $aRAc5sZcdPRNjfrTK9pchLQrJN4XkzV4eckG

Merkle Root

7e10636825a6ebb9c2cc549391fff7e213756cf1e5a3b17370de6bdb30010b81

Transactions (1)

Coinbase7e10636825a6eb…de6bdb30010b81

1 in → 25 out10.0800 XPM913 B

Ac5sZcdP…kzV4eckG APVGazMT…cDCk2nwA AQyr8Lw3…hs4nt3Pn ALdHh27b…XNbqrvPf AJWQ6Gkq…f63GcfrK

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.

1.019 × 10⁹¹(92-digit number)

10193823165394947078…90484002857282495999

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

1.019 × 10⁹¹(92-digit number)

10193823165394947078…90484002857282495999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.019 × 10⁹¹(92-digit number)

10193823165394947078…90484002857282496001

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

2.038 × 10⁹¹(92-digit number)

20387646330789894156…80968005714564991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.038 × 10⁹¹(92-digit number)

20387646330789894156…80968005714564992001

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

4.077 × 10⁹¹(92-digit number)

40775292661579788313…61936011429129983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.077 × 10⁹¹(92-digit number)

40775292661579788313…61936011429129984001

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

8.155 × 10⁹¹(92-digit number)

81550585323159576626…23872022858259967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.155 × 10⁹¹(92-digit number)

81550585323159576626…23872022858259968001

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

1.631 × 10⁹²(93-digit number)

16310117064631915325…47744045716519935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.631 × 10⁹²(93-digit number)

16310117064631915325…47744045716519936001

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