Block #233,397

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 5:01:21 PM · Difficulty 9.9424 · 6,565,403 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

151fe6adb58b163eaa1d8002bdcf95352735f0852ac6bdc6b6c3fbf460bea9b4

View on Chainz ↗

Height

#233,397

Difficulty

9.942445

Transactions

Size

1.81 KB

Version

Bits

09f14412

Nonce

39,344

Timestamp

10/29/2013, 5:01:21 PM

Confirmations

6,565,403

Mined by

⛏️ RoASMTaFpzW96zPQjZ1YZALrjZ9zDq3jZtyL

Merkle Root

d0ca11a5faa46d4193843b69b2d81c1d3a7f019e6336cb78c188769de7fb1039

Transactions (1)

Coinbased0ca11a5faa46d…88769de7fb1039

1 in → 50 out10.0800 XPM1.72 KB

ASMTaFpz…Dq3jZtyL ANpPrsJp…YzdEphWb ARpndEmc…Hg792kEk AQtzUSwq…htAuF3yC 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.

9.179 × 10⁸⁹(90-digit number)

91795690305300655983…92347919647964159999

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

9.179 × 10⁸⁹(90-digit number)

91795690305300655983…92347919647964159999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.179 × 10⁸⁹(90-digit number)

91795690305300655983…92347919647964160001

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

1.835 × 10⁹⁰(91-digit number)

18359138061060131196…84695839295928319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.835 × 10⁹⁰(91-digit number)

18359138061060131196…84695839295928320001

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

3.671 × 10⁹⁰(91-digit number)

36718276122120262393…69391678591856639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.671 × 10⁹⁰(91-digit number)

36718276122120262393…69391678591856640001

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

7.343 × 10⁹⁰(91-digit number)

73436552244240524786…38783357183713279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.343 × 10⁹⁰(91-digit number)

73436552244240524786…38783357183713280001

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

1.468 × 10⁹¹(92-digit number)

14687310448848104957…77566714367426559999

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