Block #287,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 9:37:10 AM · Difficulty 9.9868 · 6,523,512 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

608a2d45ecdce0141376a50411de5477320af00b889d9846dca5998f9b300232

View on Chainz ↗

Height

#287,595

Difficulty

9.986821

Transactions

Size

11.21 KB

Version

Bits

09fca047

Nonce

28,889

Timestamp

12/1/2013, 9:37:10 AM

Confirmations

6,523,512

Mined by

⛏️ kcaR?AGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

c3911c32d7dfaa73a0fb62f5529a1f2b04d0c25a4cb3fb57ced171b0f8713b29

Transactions (4)

Coinbased666b794b52c0f…de2e2e98f36c53

1 in → 30 out9.9900 XPM1.06 KB

AGFAJ5YL…ZEnBbk6G AZ2pPuKg…95SN2Yr7 AHuJ9wYh…BGmgHrKZ AWZd1qVJ…9pj9yfPa AKEwr54i…9BfmMkRh

9ba37ad087a118…7af35f05c72ca8

58 in → 2 out100.0346 XPM8.46 KB

AUmtjo1K…ETL3f4hP ARiw6vN9…e3ckDGkA

d26e28bebb6189…1c251adf01360c

9 in → 2 out11.0108 XPM1.38 KB

AXEBNNcS…4FopSeij APNQYaGC…odxqm1da

d162c7d4bfbc7b…378e24addd8b70

1 in → 2 out6.9502 XPM226 B

ANLNdiTn…Lw8MRNw8 ATqDht7F…xHD53DYv

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.

7.582 × 10⁹³(94-digit number)

75824849468122173752…22134382693073295359

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

7.582 × 10⁹³(94-digit number)

75824849468122173752…22134382693073295359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.582 × 10⁹³(94-digit number)

75824849468122173752…22134382693073295361

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

1.516 × 10⁹⁴(95-digit number)

15164969893624434750…44268765386146590719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.516 × 10⁹⁴(95-digit number)

15164969893624434750…44268765386146590721

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

3.032 × 10⁹⁴(95-digit number)

30329939787248869500…88537530772293181439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.032 × 10⁹⁴(95-digit number)

30329939787248869500…88537530772293181441

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

6.065 × 10⁹⁴(95-digit number)

60659879574497739001…77075061544586362879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.065 × 10⁹⁴(95-digit number)

60659879574497739001…77075061544586362881

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

1.213 × 10⁹⁵(96-digit number)

12131975914899547800…54150123089172725759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.213 × 10⁹⁵(96-digit number)

12131975914899547800…54150123089172725761

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 #287,595

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