Block #112,587

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 1:42:57 AM · Difficulty 9.7236 · 6,714,122 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08540242d98982717e430277fc52af620b247294baf2b6c6c020a79b3a911df6

View on Chainz ↗

Height

#112,587

Difficulty

9.723615

Transactions

Size

358 B

Version

Bits

09b93ed1

Nonce

35,815

Timestamp

8/12/2013, 1:42:57 AM

Confirmations

6,714,122

Mined by

⛏️ P2SHAKErQXMSbzQTkoT3CyUmWJvi8LJWgaCTzm

Merkle Root

2fe2f54676246b8664db1c31a6bc67d6a2a643108408aa2c3739db4c7d4f0b86

Transactions (2)

Coinbasee8f7354c72a28f…b36b8e5352d5d7

1 in → 1 out10.5700 XPM109 B

AKErQXMS…JWgaCTzm

a95843db21c1a2…6122538a5b3e9c

1 in → 1 out10.6900 XPM158 B

AH9D5N1B…4NXoLsWQ

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.

1.275 × 10⁹⁸(99-digit number)

12753736404884729854…65031344071105186269

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

1.275 × 10⁹⁸(99-digit number)

12753736404884729854…65031344071105186269

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10⁹⁸(99-digit number)

12753736404884729854…65031344071105186271

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

2.550 × 10⁹⁸(99-digit number)

25507472809769459709…30062688142210372539

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.550 × 10⁹⁸(99-digit number)

25507472809769459709…30062688142210372541

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

5.101 × 10⁹⁸(99-digit number)

51014945619538919419…60125376284420745079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.101 × 10⁹⁸(99-digit number)

51014945619538919419…60125376284420745081

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

1.020 × 10⁹⁹(100-digit number)

10202989123907783883…20250752568841490159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁹(100-digit number)

10202989123907783883…20250752568841490161

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

2.040 × 10⁹⁹(100-digit number)

20405978247815567767…40501505137682980319

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 #112,587

Cookie Preferences