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Block #245,688

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 3:17:35 PM · Difficulty 9.9640 · 6,571,199 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5a1eb5cf5b36ea4b1095d67b595cfa428bb7c9eec0a78f6628fa05cb7e492d5b

View on Chainz ↗

Height

#245,688

Difficulty

9.964043

Transactions

Size

423 B

Version

Bits

09f6cb7f

Nonce

106,200

Timestamp

11/5/2013, 3:17:35 PM

Confirmations

6,571,199

Merkle Root

0340f3efffe403741b6f8f3dbff675b4e0f35720156392b248d87ce5e92f955b

Transactions (2)

Coinbase7b664de3b6d036…dcfb2cab38f482

1 in → 1 out10.0700 XPM109 B

AX2TVgXP…4oFqomRn

7822a5852eee96…cf22a3f4d57654

1 in → 2 out0.8810 XPM226 B

AaG1hiyh…qK33WhUp AV6w5oLy…4FgyYe1C

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.

6.880 × 10⁹⁰(91-digit number)

68803489388182136683…55924333060656482160

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

6.880 × 10⁹⁰(91-digit number)

68803489388182136683…55924333060656482159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.880 × 10⁹⁰(91-digit number)

68803489388182136683…55924333060656482161

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

1.376 × 10⁹¹(92-digit number)

13760697877636427336…11848666121312964319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.376 × 10⁹¹(92-digit number)

13760697877636427336…11848666121312964321

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

2.752 × 10⁹¹(92-digit number)

27521395755272854673…23697332242625928639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.752 × 10⁹¹(92-digit number)

27521395755272854673…23697332242625928641

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

5.504 × 10⁹¹(92-digit number)

55042791510545709346…47394664485251857279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.504 × 10⁹¹(92-digit number)

55042791510545709346…47394664485251857281

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

1.100 × 10⁹²(93-digit number)

11008558302109141869…94789328970503714559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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.

View full Prime Chain Discovery page →

★☆☆☆☆

Rarity

CommonChain length 9

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 245688

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 5a1eb5cf5b36ea4b1095d67b595cfa428bb7c9eec0a78f6628fa05cb7e492d5b

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #245,688 on Chainz ↗

Block #245,688

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