Block #1,024,797

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/20/2015, 9:38:17 AM · Difficulty 10.7543 · 5,792,309 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de1e79149f0a110a3b776b7b093fb7a3ed57dd31196215e7df09843ab0f82865

View on Chainz ↗

Height

#1,024,797

Difficulty

10.754325

Transactions

Size

10.04 KB

Version

Bits

0ac11b78

Nonce

734,897,405

Timestamp

4/20/2015, 9:38:17 AM

Confirmations

5,792,309

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5a87635062e4f9634378311b6b1f3f636bc6a4fa1f908848a1cf8cec7f5ae2c0

Transactions (3)

Coinbasee5d1f03baf8b03…a00ec119b6a086

1 in → 1 out8.9100 XPM116 B

ANSXnLY2…Sd25TjkD

d119040a000a16…d0725947d18124

26 in → 2 out3000.0100 XPM3.84 KB

AZvpBZP5…AiKbF5g1 AZ8DQFif…QRDEaZsT

fa84f4f6d089cf…2c8e81d143e93c

41 in → 2 out2000.0100 XPM6.00 KB

AZvpBZP5…AiKbF5g1 AayQ2Zcc…JQ9mThg5

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.

8.830 × 10⁹⁶(97-digit number)

88305535353633706235…86781774176604350719

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

8.830 × 10⁹⁶(97-digit number)

88305535353633706235…86781774176604350719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.830 × 10⁹⁶(97-digit number)

88305535353633706235…86781774176604350721

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

1.766 × 10⁹⁷(98-digit number)

17661107070726741247…73563548353208701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.766 × 10⁹⁷(98-digit number)

17661107070726741247…73563548353208701441

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

3.532 × 10⁹⁷(98-digit number)

35322214141453482494…47127096706417402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.532 × 10⁹⁷(98-digit number)

35322214141453482494…47127096706417402881

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

7.064 × 10⁹⁷(98-digit number)

70644428282906964988…94254193412834805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.064 × 10⁹⁷(98-digit number)

70644428282906964988…94254193412834805761

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

1.412 × 10⁹⁸(99-digit number)

14128885656581392997…88508386825669611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.412 × 10⁹⁸(99-digit number)

14128885656581392997…88508386825669611521

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 #1,024,797

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