Home/Chain Registry/Block #245,964

Block #245,964

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 7:15:39 PM · Difficulty 9.9644 · 6,584,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a864fc1615db23291ea7a78eab4bbe678f9b2ef5649310f2778e19747aabf980

View on Chainz ↗

Height

#245,964

Difficulty

9.964350

Transactions

Size

601 B

Version

Bits

09f6dfa9

Nonce

20,739

Timestamp

11/5/2013, 7:15:39 PM

Confirmations

6,584,839

Merkle Root

10fd4204c6d106c4ef35b40b51524fdb58fa4c3edeacc1e872a2127ad14ebebb

Transactions (2)

Coinbasecf9c0a5cd68380…46610f9b45591b

1 in → 2 out10.0700 XPM136 B

AZDUEbdS…RYKMRZET ASNt3cJa…L5zCqAYM

bfbdcae8fbc852…b7d771fbe4bd8e

2 in → 2 out162.0100 XPM374 B

AXrskf2K…VNwP1WEf AdnmAQ5N…QcLHGf1v

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.

3.955 × 10⁹⁶(97-digit number)

39559420800018328074…14370020465360031560

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

3.955 × 10⁹⁶(97-digit number)

39559420800018328074…14370020465360031559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.955 × 10⁹⁶(97-digit number)

39559420800018328074…14370020465360031561

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

7.911 × 10⁹⁶(97-digit number)

79118841600036656149…28740040930720063119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.911 × 10⁹⁶(97-digit number)

79118841600036656149…28740040930720063121

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

1.582 × 10⁹⁷(98-digit number)

15823768320007331229…57480081861440126239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.582 × 10⁹⁷(98-digit number)

15823768320007331229…57480081861440126241

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

3.164 × 10⁹⁷(98-digit number)

31647536640014662459…14960163722880252479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.164 × 10⁹⁷(98-digit number)

31647536640014662459…14960163722880252481

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

6.329 × 10⁹⁷(98-digit number)

63295073280029324919…29920327445760504959

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 245964

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 a864fc1615db23291ea7a78eab4bbe678f9b2ef5649310f2778e19747aabf980

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 #245,964 on Chainz ↗

Block #245,964

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