Block #367,508

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 3:27:40 AM · Difficulty 10.4336 · 6,437,771 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec8ed8d3b9e97ee1255f49e561b3641144b4f2de8303427df146284d01d30c90

View on Chainz ↗

Height

#367,508

Difficulty

10.433638

Transactions

Size

766 B

Version

Bits

0a6f02e3

Nonce

3,773

Timestamp

1/20/2014, 3:27:40 AM

Confirmations

6,437,771

Mined by

⛏️ pAM4c6u8dYeQBkdo3RbtZ8WqY8DwUNSLEd4

Merkle Root

bc855a48f9a8462f62fd618a1d6fba038584d34e25868e85df9bd7d3950ccfa5

Transactions (1)

Coinbasebc855a48f9a846…9bd7d3950ccfa5

1 in → 18 out9.1700 XPM675 B

AM4c6u8d…wUNSLEd4 AFutDVqJ…TJTJj6UF AShKwBPr…M993r1eU Acs9SHrk…QJSB8SFG AbiuqgvC…zjLCTyEz

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.

5.792 × 10⁹⁵(96-digit number)

57926441567384470627…41908030325277784959

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

5.792 × 10⁹⁵(96-digit number)

57926441567384470627…41908030325277784959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.792 × 10⁹⁵(96-digit number)

57926441567384470627…41908030325277784961

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

1.158 × 10⁹⁶(97-digit number)

11585288313476894125…83816060650555569919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.158 × 10⁹⁶(97-digit number)

11585288313476894125…83816060650555569921

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

2.317 × 10⁹⁶(97-digit number)

23170576626953788250…67632121301111139839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.317 × 10⁹⁶(97-digit number)

23170576626953788250…67632121301111139841

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

4.634 × 10⁹⁶(97-digit number)

46341153253907576501…35264242602222279679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.634 × 10⁹⁶(97-digit number)

46341153253907576501…35264242602222279681

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

9.268 × 10⁹⁶(97-digit number)

92682306507815153003…70528485204444559359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.268 × 10⁹⁶(97-digit number)

92682306507815153003…70528485204444559361

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