Block #25,946

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 3:48:13 AM · Difficulty 7.9731 · 6,763,621 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f97c1d344e4cd13cb3dc48568b8d8317b5c22df2fe8f0d3f23a4414f93f11f71

View on Chainz ↗

Height

#25,946

Difficulty

7.973120

Transactions

Size

2.55 KB

Version

Bits

07f91e5d

Nonce

248

Timestamp

7/13/2013, 3:48:13 AM

Confirmations

6,763,621

Merkle Root

b350d317d440ace0f8797ffa5a2566668c87043b785fc0d7e2ecde458d2cb225

Transactions (2)

Coinbase7f957489f26c27…4004cab247c608

1 in → 1 out15.7400 XPM108 B

AWdtCUuJ…HscHZriH

18790f7d8aa3e9…57f3227d10b908

20 in → 2 out403.9000 XPM2.36 KB

AdhRYkdk…qwNrcYxb Ac4udheJ…tqqNYAdo

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.

5.479 × 10⁸³(84-digit number)

54797731543181221471…38870567110787855919

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

5.479 × 10⁸³(84-digit number)

54797731543181221471…38870567110787855919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.479 × 10⁸³(84-digit number)

54797731543181221471…38870567110787855921

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

1.095 × 10⁸⁴(85-digit number)

10959546308636244294…77741134221575711839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.095 × 10⁸⁴(85-digit number)

10959546308636244294…77741134221575711841

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

2.191 × 10⁸⁴(85-digit number)

21919092617272488588…55482268443151423679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.191 × 10⁸⁴(85-digit number)

21919092617272488588…55482268443151423681

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

4.383 × 10⁸⁴(85-digit number)

43838185234544977177…10964536886302847359

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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