Block #258,103

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/12/2013, 8:39:10 PM · Difficulty 9.9762 · 6,537,806 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84c3eed2c1afd00cdfeafdc953e33aa347f8bf41c0d3112ad5ec060e9bb86f51

View on Chainz ↗

Height

#258,103

Difficulty

9.976220

Transactions

Size

1.71 KB

Version

Bits

09f9e988

Nonce

9,720

Timestamp

11/12/2013, 8:39:10 PM

Confirmations

6,537,806

Mined by

⛏️ 7aRDAd9uUqPHBW4X1ENp8We6cWhToUmMTnTyRy

Merkle Root

ee390eb6e04562677552c3ebfe97a847a83d467e36314ce102ef5f4fdafa0342

Transactions (1)

Coinbaseee390eb6e04562…ef5f4fdafa0342

1 in → 47 out10.0100 XPM1.62 KB

Ad9uUqPH…mMTnTyRy ANuKx9Ke…wm7nrBRq AQtzUSwq…htAuF3yC APZy8y6E…QZaGQjfp ARR7aRH6…ne3DXGXZ

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.

1.242 × 10⁹⁰(91-digit number)

12424540055606586334…48750841990084452999

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

1.242 × 10⁹⁰(91-digit number)

12424540055606586334…48750841990084452999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.242 × 10⁹⁰(91-digit number)

12424540055606586334…48750841990084453001

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

2.484 × 10⁹⁰(91-digit number)

24849080111213172668…97501683980168905999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.484 × 10⁹⁰(91-digit number)

24849080111213172668…97501683980168906001

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

4.969 × 10⁹⁰(91-digit number)

49698160222426345336…95003367960337811999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.969 × 10⁹⁰(91-digit number)

49698160222426345336…95003367960337812001

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

9.939 × 10⁹⁰(91-digit number)

99396320444852690672…90006735920675623999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.939 × 10⁹⁰(91-digit number)

99396320444852690672…90006735920675624001

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

1.987 × 10⁹¹(92-digit number)

19879264088970538134…80013471841351247999

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