Home/Chain Registry/Block #253,750

Block #253,750

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/10/2013, 8:09:56 AM · Difficulty 9.9724 · 6,558,326 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

603be9e59dad4229f021f0b72cf0d08307814d9a3993b8e3047e94cd9b8983c2

View on Chainz ↗

Height

#253,750

Difficulty

9.972430

Transactions

Size

1.44 KB

Version

Bits

09f8f133

Nonce

666,046

Timestamp

11/10/2013, 8:09:56 AM

Confirmations

6,558,326

Merkle Root

3572cbabeebe2c22ce8f5705e388a628d1c5f45572a3c728224ffd642e2e76e7

Transactions (1)

Coinbase3572cbabeebe2c…4ffd642e2e76e7

1 in → 39 out10.0200 XPM1.36 KB

ARanXFdq…2FNquU2w ANuKx9Ke…wm7nrBRq ALFWpHxd…zhX7LjhL AJaGRnaj…iCHGoy6E APVGazMT…cDCk2nwA

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.

3.981 × 10⁹²(93-digit number)

39812047053048558342…73151225900734412800

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

3.981 × 10⁹²(93-digit number)

39812047053048558342…73151225900734412799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.981 × 10⁹²(93-digit number)

39812047053048558342…73151225900734412801

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

7.962 × 10⁹²(93-digit number)

79624094106097116684…46302451801468825599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.962 × 10⁹²(93-digit number)

79624094106097116684…46302451801468825601

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

1.592 × 10⁹³(94-digit number)

15924818821219423336…92604903602937651199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.592 × 10⁹³(94-digit number)

15924818821219423336…92604903602937651201

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

3.184 × 10⁹³(94-digit number)

31849637642438846673…85209807205875302399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.184 × 10⁹³(94-digit number)

31849637642438846673…85209807205875302401

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

6.369 × 10⁹³(94-digit number)

63699275284877693347…70419614411750604799

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 253750

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 603be9e59dad4229f021f0b72cf0d08307814d9a3993b8e3047e94cd9b8983c2

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 #253,750 on Chainz ↗

Block #253,750

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