Block #360,410

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 10:46:12 AM · Difficulty 10.3914 · 6,443,215 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc778ac026bcc3683f07f1008a9a26aebc287e96f39d1319b15a66facdfa4da1

View on Chainz ↗

Height

#360,410

Difficulty

10.391361

Transactions

Size

1.15 KB

Version

Bits

0a643034

Nonce

34,376

Timestamp

1/15/2014, 10:46:12 AM

Confirmations

6,443,215

Mined by

⛏️ xAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

38efd0bd3c7bfa815b0f2b0ae65682a912507fa350496394cb7e1ae96fe5e856

Transactions (3)

Coinbased7716ee550ee92…375f743bee6e3e

1 in → 17 out9.2700 XPM641 B

AFutDVqJ…TJTJj6UF AMHMrUuK…jgEj6HLr AShKwBPr…M993r1eU AJdLNXdT…prit4boi AXHFULNN…K5pjYXqj

f89b9ea7176030…1ecce3caab2885

1 in → 2 out3.0385 XPM226 B

AaZKg6k8…2o9fXvX7 ANHjm2XJ…XVe8kxaU

1fd609c3b8c100…623f650becbc8d

1 in → 2 out3.1218 XPM225 B

ATQWTYWU…KFEiavZW ALHbRxMJ…LEi9pifp

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.

7.472 × 10⁹⁴(95-digit number)

74724480103654528369…86982640123200134239

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

7.472 × 10⁹⁴(95-digit number)

74724480103654528369…86982640123200134239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.472 × 10⁹⁴(95-digit number)

74724480103654528369…86982640123200134241

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

1.494 × 10⁹⁵(96-digit number)

14944896020730905673…73965280246400268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.494 × 10⁹⁵(96-digit number)

14944896020730905673…73965280246400268481

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

2.988 × 10⁹⁵(96-digit number)

29889792041461811347…47930560492800536959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.988 × 10⁹⁵(96-digit number)

29889792041461811347…47930560492800536961

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

5.977 × 10⁹⁵(96-digit number)

59779584082923622695…95861120985601073919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.977 × 10⁹⁵(96-digit number)

59779584082923622695…95861120985601073921

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

1.195 × 10⁹⁶(97-digit number)

11955916816584724539…91722241971202147839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.195 × 10⁹⁶(97-digit number)

11955916816584724539…91722241971202147841

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