Block #203,458

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/10/2013, 8:49:48 PM · Difficulty 9.8974 · 6,607,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e8d446719e5f8b0b3fc1d104b4f86d519ce98eac3c0c43b846a0398e00524f05

View on Chainz ↗

Height

#203,458

Difficulty

9.897371

Transactions

Size

539 B

Version

Bits

09e5ba21

Nonce

33,988

Timestamp

10/10/2013, 8:49:48 PM

Confirmations

6,607,035

Mined by

⛏️ P2SHANqDHpCLzKoFpjajLeWGRLPKVamNDkx51q

Merkle Root

9e09299a259d017cd66a154c90795cdd83bdc15041a31f889f2e39cb7d631f38

Transactions (2)

Coinbase0bd1eacb2639a5…bc684705b139a9

1 in → 1 out10.2000 XPM109 B

ANqDHpCL…mNDkx51q

674ef9af80ec90…a23e225d734a82

2 in → 1 out5.9837 XPM341 B

Ab2EJo7A…GbDZf26e

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.

9.424 × 10⁹¹(92-digit number)

94242181592725217035…74957935705945845119

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

9.424 × 10⁹¹(92-digit number)

94242181592725217035…74957935705945845119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.424 × 10⁹¹(92-digit number)

94242181592725217035…74957935705945845121

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

1.884 × 10⁹²(93-digit number)

18848436318545043407…49915871411891690239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.884 × 10⁹²(93-digit number)

18848436318545043407…49915871411891690241

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

3.769 × 10⁹²(93-digit number)

37696872637090086814…99831742823783380479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.769 × 10⁹²(93-digit number)

37696872637090086814…99831742823783380481

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

7.539 × 10⁹²(93-digit number)

75393745274180173628…99663485647566760959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.539 × 10⁹²(93-digit number)

75393745274180173628…99663485647566760961

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

1.507 × 10⁹³(94-digit number)

15078749054836034725…99326971295133521919

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

Block #203,458

Cookie Preferences