Block #233,801

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 10:47:33 PM · Difficulty 9.9431 · 6,558,088 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

544984a88e0d87dd3a86bae636ef5560faa5d19132e238770e8fc77c45681792

View on Chainz ↗

Height

#233,801

Difficulty

9.943108

Transactions

Size

1.84 KB

Version

Bits

09f16f82

Nonce

7,394

Timestamp

10/29/2013, 10:47:33 PM

Confirmations

6,558,088

Merkle Root

634a89040bd14359498589ade5fa6a6b96a0943befcf95185acf9683ec209d86

Transactions (1)

Coinbase634a89040bd143…cf9683ec209d86

1 in → 51 out10.0800 XPM1.75 KB

AFwHRcHo…HAieUvYT AFqKfjez…qX9Ace3g AdwTEXyC…NwbVbqZV ANuKx9Ke…wm7nrBRq ARpndEmc…Hg792kEk

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.

3.451 × 10⁹¹(92-digit number)

34515371922211920587…40725522777331978239

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

3.451 × 10⁹¹(92-digit number)

34515371922211920587…40725522777331978239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.451 × 10⁹¹(92-digit number)

34515371922211920587…40725522777331978241

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

6.903 × 10⁹¹(92-digit number)

69030743844423841175…81451045554663956479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.903 × 10⁹¹(92-digit number)

69030743844423841175…81451045554663956481

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

1.380 × 10⁹²(93-digit number)

13806148768884768235…62902091109327912959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.380 × 10⁹²(93-digit number)

13806148768884768235…62902091109327912961

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

2.761 × 10⁹²(93-digit number)

27612297537769536470…25804182218655825919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.761 × 10⁹²(93-digit number)

27612297537769536470…25804182218655825921

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

5.522 × 10⁹²(93-digit number)

55224595075539072940…51608364437311651839

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