Block #2,394,905

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/25/2017, 5:07:53 PM · Difficulty 10.8726 · 4,414,370 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

258742dea1e5fe0dcaab0aa03303ae615e8d3f261291876e2577232ffb165016

View on Chainz ↗

Height

#2,394,905

Difficulty

10.872611

Transactions

Size

236 B

Version

Bits

0adf636b

Nonce

680

Timestamp

11/25/2017, 5:07:53 PM

Confirmations

4,414,370

Mined by

⛏️ P2SHAYKurbGZFQGjWoMj1QGCcPh3ZcigxnTApb

Merkle Root

23ceb5c1ba7eb6c36809b74a079813a980648060bc67ad7241f59e86e213f2d6

Transactions (1)

Coinbase23ceb5c1ba7eb6…f59e86e213f2d6

1 in → 2 out8.4500 XPM145 B

AYKurbGZ…igxnTApb APRimehp…nwGYffXK

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.

3.724 × 10⁹⁶(97-digit number)

37240035011980020039…32448697667101513439

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

3.724 × 10⁹⁶(97-digit number)

37240035011980020039…32448697667101513439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.724 × 10⁹⁶(97-digit number)

37240035011980020039…32448697667101513441

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

7.448 × 10⁹⁶(97-digit number)

74480070023960040079…64897395334203026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.448 × 10⁹⁶(97-digit number)

74480070023960040079…64897395334203026881

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

1.489 × 10⁹⁷(98-digit number)

14896014004792008015…29794790668406053759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.489 × 10⁹⁷(98-digit number)

14896014004792008015…29794790668406053761

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

2.979 × 10⁹⁷(98-digit number)

29792028009584016031…59589581336812107519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.979 × 10⁹⁷(98-digit number)

29792028009584016031…59589581336812107521

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

5.958 × 10⁹⁷(98-digit number)

59584056019168032063…19179162673624215039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.958 × 10⁹⁷(98-digit number)

59584056019168032063…19179162673624215041

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 #2,394,905

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