Block #181,112

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/26/2013, 7:55:54 AM · Difficulty 9.8606 · 6,624,067 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

72b445aef39ad3b3757e2c46e550a1ed6d88b1859c17615a6ed2ee57892b4a0d

View on Chainz ↗

Height

#181,112

Difficulty

9.860632

Transactions

Size

574 B

Version

Bits

09dc5267

Nonce

6,386

Timestamp

9/26/2013, 7:55:54 AM

Confirmations

6,624,067

Mined by

⛏️ P2SHAJgHpa8bWXAnCbvBMmWEijC8R51N2Bhnd4

Merkle Root

69e6130b73de64cd68cfbbe6784b06ca7c47e1734500377589c5d3bcb3a6541f

Transactions (2)

Coinbase16ce72a65fd8af…c0c87634443504

1 in → 1 out10.2800 XPM109 B

AJgHpa8b…1N2Bhnd4

c143cd9d2ae9f2…cd44ee63287bfe

2 in → 2 out3.2434 XPM374 B

ANvtpRa1…QjsraDJz AGaKkABV…XGSDBNzn

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.

4.893 × 10⁹⁷(98-digit number)

48934158395559687104…80826550345860626239

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

4.893 × 10⁹⁷(98-digit number)

48934158395559687104…80826550345860626239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.893 × 10⁹⁷(98-digit number)

48934158395559687104…80826550345860626241

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

9.786 × 10⁹⁷(98-digit number)

97868316791119374209…61653100691721252479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.786 × 10⁹⁷(98-digit number)

97868316791119374209…61653100691721252481

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

1.957 × 10⁹⁸(99-digit number)

19573663358223874841…23306201383442504959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.957 × 10⁹⁸(99-digit number)

19573663358223874841…23306201383442504961

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

3.914 × 10⁹⁸(99-digit number)

39147326716447749683…46612402766885009919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.914 × 10⁹⁸(99-digit number)

39147326716447749683…46612402766885009921

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

7.829 × 10⁹⁸(99-digit number)

78294653432895499367…93224805533770019839

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