Block #236,123

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/31/2013, 8:03:35 AM · Difficulty 9.9468 · 6,559,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

39c7bac3a74ca6b1c833ceb1bd9549f7e487d798b699624be0830bb2c43b8d0e

View on Chainz ↗

Height

#236,123

Difficulty

9.946761

Transactions

Size

1.81 KB

Version

Bits

09f25ef6

Nonce

82,153

Timestamp

10/31/2013, 8:03:35 AM

Confirmations

6,559,771

Mined by

⛏️ RrYAGHsFFzKwG1bYVWPDJXUqcJw8d3J7QNqtQ

Merkle Root

3c86f20e7558defae72846fbbdd77b921b5e882c569ced783c243113911291b2

Transactions (1)

Coinbase3c86f20e7558de…243113911291b2

1 in → 50 out10.0700 XPM1.72 KB

AGHsFFzK…3J7QNqtQ Aaox8Rxx…XTyyJXVx AQapNBe8…Pxk4vkev AQtzUSwq…htAuF3yC AG9H2B8p…eiaSPdGS

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.

1.894 × 10⁹¹(92-digit number)

18948255187938778049…06331358263374530239

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

1.894 × 10⁹¹(92-digit number)

18948255187938778049…06331358263374530239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.894 × 10⁹¹(92-digit number)

18948255187938778049…06331358263374530241

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

3.789 × 10⁹¹(92-digit number)

37896510375877556099…12662716526749060479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.789 × 10⁹¹(92-digit number)

37896510375877556099…12662716526749060481

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

7.579 × 10⁹¹(92-digit number)

75793020751755112199…25325433053498120959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.579 × 10⁹¹(92-digit number)

75793020751755112199…25325433053498120961

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

1.515 × 10⁹²(93-digit number)

15158604150351022439…50650866106996241919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.515 × 10⁹²(93-digit number)

15158604150351022439…50650866106996241921

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

3.031 × 10⁹²(93-digit number)

30317208300702044879…01301732213992483839

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