Block #247,267

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/6/2013, 4:00:04 PM · Difficulty 9.9648 · 6,543,726 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6dc07e4bb188cc94783a76263deb0ed2cb9a3863a429a9bc5cd93abb8e6307b7

View on Chainz ↗

Height

#247,267

Difficulty

9.964798

Transactions

Size

990 B

Version

Bits

09f6fcff

Nonce

11,809

Timestamp

11/6/2013, 4:00:04 PM

Confirmations

6,543,726

Merkle Root

7230303468548b983a5f50bc307a17c310367d9e8eeade4719b255dee66ebb51

Transactions (4)

Coinbased5ecc485ef65ef…5ce5fdb3a3f74c

1 in → 2 out10.0900 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

e0a13a2be85bbf…e67da00282ec44

1 in → 1 out10.0500 XPM159 B

AbP1iY2S…QXTtEVYb

6d7a3e9b7631b5…78bd88086f4df6

2 in → 2 out11.9127 XPM374 B

ANBFe6hj…Gd39JrrZ AaYBJ5QB…D82bB7Rd

4c8596e42f82e1…086601f63d6887

1 in → 2 out5.2639 XPM226 B

AWeGCtdP…9mP117Lb ASnSjgQg…fewAaNPL

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.

1.476 × 10⁹⁵(96-digit number)

14762271380359985626…65420344310623672399

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

1.476 × 10⁹⁵(96-digit number)

14762271380359985626…65420344310623672399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.476 × 10⁹⁵(96-digit number)

14762271380359985626…65420344310623672401

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

2.952 × 10⁹⁵(96-digit number)

29524542760719971252…30840688621247344799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.952 × 10⁹⁵(96-digit number)

29524542760719971252…30840688621247344801

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

5.904 × 10⁹⁵(96-digit number)

59049085521439942505…61681377242494689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.904 × 10⁹⁵(96-digit number)

59049085521439942505…61681377242494689601

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

1.180 × 10⁹⁶(97-digit number)

11809817104287988501…23362754484989379199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.180 × 10⁹⁶(97-digit number)

11809817104287988501…23362754484989379201

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

2.361 × 10⁹⁶(97-digit number)

23619634208575977002…46725508969978758399

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