Block #235,081

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 5:18:14 PM · Difficulty 9.9450 · 6,560,327 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8bdcc9b3b35d389d7e6223cddfefe67c37e490864e523c67e499f19fa20c2d8f

View on Chainz ↗

Height

#235,081

Difficulty

9.945038

Transactions

Size

1.97 KB

Version

Bits

09f1ee0b

Nonce

21,890

Timestamp

10/30/2013, 5:18:14 PM

Confirmations

6,560,327

Mined by

⛏️ IRq?P5AKFMENK8Y83ntTmGeVC63vAJZ8b6knxLfH

Merkle Root

ebba226a9d18e64cb04293d2c59511e758e0af32ee8c7e81e6e4b1f36775b13d

Transactions (1)

Coinbaseebba226a9d18e6…e4b1f36775b13d

1 in → 55 out10.0800 XPM1.89 KB

AKFMENK8…b6knxLfH ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC ANUaggy4…MWdrertQ AU9KdB9r…o5XC6WMy

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.

2.646 × 10⁹⁴(95-digit number)

26468604573978475419…99998154815968433599

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

2.646 × 10⁹⁴(95-digit number)

26468604573978475419…99998154815968433599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.646 × 10⁹⁴(95-digit number)

26468604573978475419…99998154815968433601

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

5.293 × 10⁹⁴(95-digit number)

52937209147956950838…99996309631936867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.293 × 10⁹⁴(95-digit number)

52937209147956950838…99996309631936867201

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

1.058 × 10⁹⁵(96-digit number)

10587441829591390167…99992619263873734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.058 × 10⁹⁵(96-digit number)

10587441829591390167…99992619263873734401

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

2.117 × 10⁹⁵(96-digit number)

21174883659182780335…99985238527747468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.117 × 10⁹⁵(96-digit number)

21174883659182780335…99985238527747468801

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

4.234 × 10⁹⁵(96-digit number)

42349767318365560670…99970477055494937599

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