Home/Chain Registry/Block #245,546

Block #245,546

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 1:03:54 PM · Difficulty 9.9640 · 6,550,624 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0641b25d0b832e43abdf20d36a8db7cb3eea4012b378091ce64e114626c2e7c

View on Chainz ↗

Height

#245,546

Difficulty

9.963977

Transactions

Size

754 B

Version

Bits

09f6c72d

Nonce

32,466

Timestamp

11/5/2013, 1:03:54 PM

Confirmations

6,550,624

Merkle Root

4c1c155f01835db658b8700e57aca93423e4abdd35db0cdec50a064ddd4a1316

Transactions (2)

Coinbase221d99cfd6b7c6…b4427ba41a8b82

1 in → 2 out10.0800 XPM141 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

d17e76d3117f47…fbbf9138d76b69

3 in → 2 out123.5900 XPM522 B

AYNfgPS1…hf1xjfSb Aak6zVqa…ognn4QKX

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.

3.935 × 10⁹⁶(97-digit number)

39351381370746088818…64738375512197673600

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

3.935 × 10⁹⁶(97-digit number)

39351381370746088818…64738375512197673599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.935 × 10⁹⁶(97-digit number)

39351381370746088818…64738375512197673601

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

7.870 × 10⁹⁶(97-digit number)

78702762741492177636…29476751024395347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.870 × 10⁹⁶(97-digit number)

78702762741492177636…29476751024395347201

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

1.574 × 10⁹⁷(98-digit number)

15740552548298435527…58953502048790694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.574 × 10⁹⁷(98-digit number)

15740552548298435527…58953502048790694401

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

3.148 × 10⁹⁷(98-digit number)

31481105096596871054…17907004097581388799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.148 × 10⁹⁷(98-digit number)

31481105096596871054…17907004097581388801

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

6.296 × 10⁹⁷(98-digit number)

62962210193193742109…35814008195162777599

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 245546

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 c0641b25d0b832e43abdf20d36a8db7cb3eea4012b378091ce64e114626c2e7c

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 #245,546 on Chainz ↗