Block #271,558

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 5:06:52 PM · Difficulty 9.9520 · 6,533,717 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

412244f7701ee96460e436641c3eedfc979d8639309b033e523b9acdc80a22bc

View on Chainz ↗

Height

#271,558

Difficulty

9.952043

Transactions

Size

2.30 KB

Version

Bits

09f3b914

Nonce

508,809

Timestamp

11/24/2013, 5:06:52 PM

Confirmations

6,533,717

Mined by

⛏️ P2SHAf6jLHoedN5WbQAdocRbqms44S1TFijxC7

Merkle Root

a6c91baad435d8556b262a22fbc90cd67b5884a1eeef16fc17fb05807db69401

Transactions (5)

Coinbasef9abe092503289…437bce732d2801

1 in → 1 out10.1300 XPM109 B

Af6jLHoe…1TFijxC7

2fe08e0fa086ba…a8ce7f17d2c515

1 in → 2 out8.0465 XPM225 B

AYTS72kz…TPLrvcVF AcGfgBbB…wXXM6hRs

c5911e1364dff8…cca1272073afc5

1 in → 2 out7.9904 XPM226 B

AbFnzt5S…1dPz3N7o AdUsA5Y5…V5jnBPBW

d395cc0aef4696…d2ed72ac7bae02

6 in → 4 out9.3359 XPM1.01 KB

AaFS89S8…Cn1Z5yA4 AMuPGPXT…eMMNvd8v AK3vz3dH…9NvorskL AeKNrjNj…1NEq95Ta

981547f3b2d216…5ece0d85a9b858

4 in → 2 out5.1914 XPM670 B

AJbiYmfP…oJ8Dusne AM28L7rw…RCYL5aQa

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.

5.934 × 10⁹²(93-digit number)

59344707125404873447…30732579844012418209

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

5.934 × 10⁹²(93-digit number)

59344707125404873447…30732579844012418209

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.934 × 10⁹²(93-digit number)

59344707125404873447…30732579844012418211

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

1.186 × 10⁹³(94-digit number)

11868941425080974689…61465159688024836419

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.186 × 10⁹³(94-digit number)

11868941425080974689…61465159688024836421

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

2.373 × 10⁹³(94-digit number)

23737882850161949378…22930319376049672839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.373 × 10⁹³(94-digit number)

23737882850161949378…22930319376049672841

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

4.747 × 10⁹³(94-digit number)

47475765700323898757…45860638752099345679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.747 × 10⁹³(94-digit number)

47475765700323898757…45860638752099345681

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

9.495 × 10⁹³(94-digit number)

94951531400647797515…91721277504198691359

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