Block #373,197

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 3:54:46 AM · Difficulty 10.4237 · 6,433,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1690fe8549a5661a644985a9137b5851688e3edfe448e8a0b56fd39d0b73674d

View on Chainz ↗

Height

#373,197

Difficulty

10.423735

Transactions

Size

3.24 KB

Version

Bits

0a6c79ed

Nonce

781

Timestamp

1/24/2014, 3:54:46 AM

Confirmations

6,433,945

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e4c3b4086f251d0215edf86277bd3744cd74a576a51c9edf1c7f041732a8b06e

Transactions (3)

Coinbase1706a6d8de5a22…41d7d4fd454dfc

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

6fdf2b149f2bdc…0524ec34e05b9f

1 in → 2 out6.7500 XPM226 B

AHutPR2D…EghNb9Zu AQg8NwAU…8M2beH5c

181520cdd6efb0…e017289196b2ba

19 in → 2 out18.4152 XPM2.82 KB

AYuE8tHW…4eB1ecTz AbYoLR1Q…tcYrembK

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.

7.895 × 10⁹⁵(96-digit number)

78958096939746910068…77221850466737770879

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

7.895 × 10⁹⁵(96-digit number)

78958096939746910068…77221850466737770879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.895 × 10⁹⁵(96-digit number)

78958096939746910068…77221850466737770881

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

1.579 × 10⁹⁶(97-digit number)

15791619387949382013…54443700933475541759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.579 × 10⁹⁶(97-digit number)

15791619387949382013…54443700933475541761

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

3.158 × 10⁹⁶(97-digit number)

31583238775898764027…08887401866951083519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.158 × 10⁹⁶(97-digit number)

31583238775898764027…08887401866951083521

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

6.316 × 10⁹⁶(97-digit number)

63166477551797528054…17774803733902167039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.316 × 10⁹⁶(97-digit number)

63166477551797528054…17774803733902167041

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

1.263 × 10⁹⁷(98-digit number)

12633295510359505610…35549607467804334079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.263 × 10⁹⁷(98-digit number)

12633295510359505610…35549607467804334081

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

Block #373,197

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