Home/Chain Registry/Block #253,083

Block #253,083

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 10:44:23 PM · Difficulty 9.9718 · 6,538,272 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c370b63ef65f3a3436586159c85d000f2751cddf14c3bb181ab1d459d3aef1df

View on Chainz ↗

Height

#253,083

Difficulty

9.971839

Transactions

Size

209 B

Version

Bits

09f8ca70

Nonce

134,218,299

Timestamp

11/9/2013, 10:44:23 PM

Confirmations

6,538,272

Merkle Root

6a771f675cf3995e43efdfc62ad5c2dcb9ca63cfa364f61f78bc2b5a57eb8b86

Transactions (1)

Coinbase6a771f675cf399…bc2b5a57eb8b86

1 in → 1 out10.0400 XPM116 B

AcLBm5Z9…S683d7c3

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.

8.835 × 10¹⁰²(103-digit number)

88354648933405049853…35529946784282519800

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

8.835 × 10¹⁰²(103-digit number)

88354648933405049853…35529946784282519799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.835 × 10¹⁰²(103-digit number)

88354648933405049853…35529946784282519801

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

1.767 × 10¹⁰³(104-digit number)

17670929786681009970…71059893568565039599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.767 × 10¹⁰³(104-digit number)

17670929786681009970…71059893568565039601

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

3.534 × 10¹⁰³(104-digit number)

35341859573362019941…42119787137130079199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.534 × 10¹⁰³(104-digit number)

35341859573362019941…42119787137130079201

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

7.068 × 10¹⁰³(104-digit number)

70683719146724039882…84239574274260158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.068 × 10¹⁰³(104-digit number)

70683719146724039882…84239574274260158401

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

1.413 × 10¹⁰⁴(105-digit number)

14136743829344807976…68479148548520316799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.413 × 10¹⁰⁴(105-digit number)

14136743829344807976…68479148548520316801

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.

View full Prime Chain Discovery page →

★★☆☆☆

Rarity

UncommonChain length 10

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 253083

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 c370b63ef65f3a3436586159c85d000f2751cddf14c3bb181ab1d459d3aef1df

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 #253,083 on Chainz ↗