Block #362,588

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/16/2014, 7:48:25 PM · Difficulty 10.4150 · 6,440,389 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

744a5447a325cc05fdcf144ba6924a022eec90ac0a79b440eb8766a96b95d215

View on Chainz ↗

Height

#362,588

Difficulty

10.414990

Transactions

Size

1.25 KB

Version

Bits

0a6a3cc3

Nonce

123,373

Timestamp

1/16/2014, 7:48:25 PM

Confirmations

6,440,389

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

6354f729137ce7e7d41a90006929a18620b1147dd92d6365c2357ea28f8c4056

Transactions (5)

Coinbase694678afeb8972…da9e7016fdfea9

1 in → 2 out9.2400 XPM136 B

ARmAMwyu…P7Kn74ZT Abiw8n3q…ZnZfgvQW

ec33cea79e2b34…95da3a9137e47b

2 in → 2 out12.4098 XPM373 B

ATrZthfS…rCVSwYd2 AXCer4UL…PjNwKAtq

7d4ebc9a670b69…7dbe13e1f85887

1 in → 2 out5.1055 XPM226 B

AJu4geM6…GQCwqKEb AQwJeCjz…1QyBCx5P

7ae2ffdc23964c…0225eb0061e674

1 in → 2 out4.1331 XPM225 B

AJJ3Lgwt…4JguujSk AK5eMZv7…7wDmjJxU

f90c4a600731aa…6993efd830b7c8

1 in → 2 out5.0939 XPM227 B

AKmrvuK8…sKdcx7io AYXiQEyP…myu8sEHZ

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.

2.815 × 10¹⁰²(103-digit number)

28155934617603029494…66716651554080665759

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

2.815 × 10¹⁰²(103-digit number)

28155934617603029494…66716651554080665759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.815 × 10¹⁰²(103-digit number)

28155934617603029494…66716651554080665761

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

5.631 × 10¹⁰²(103-digit number)

56311869235206058989…33433303108161331519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.631 × 10¹⁰²(103-digit number)

56311869235206058989…33433303108161331521

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

1.126 × 10¹⁰³(104-digit number)

11262373847041211797…66866606216322663039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.126 × 10¹⁰³(104-digit number)

11262373847041211797…66866606216322663041

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

2.252 × 10¹⁰³(104-digit number)

22524747694082423595…33733212432645326079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.252 × 10¹⁰³(104-digit number)

22524747694082423595…33733212432645326081

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

4.504 × 10¹⁰³(104-digit number)

45049495388164847191…67466424865290652159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.504 × 10¹⁰³(104-digit number)

45049495388164847191…67466424865290652161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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