Home/Chain Registry/Block #275,590

Block #275,590

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 6:48:40 PM · Difficulty 9.9612 · 6,515,568 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bad6d3783afe7ea59c68e50702d70c95f27f9d9e1297109dbb669309f208631c

View on Chainz ↗

Height

#275,590

Difficulty

9.961179

Transactions

Size

1004 B

Version

Bits

09f60fcd

Nonce

283,447

Timestamp

11/26/2013, 6:48:40 PM

Confirmations

6,515,568

Merkle Root

1ec9e71518e578239feb21a2acdcb4a341ed36670bdb5e7d86c3aabbff2ec374

Transactions (1)

Coinbase1ec9e71518e578…c3aabbff2ec374

1 in → 25 out10.0600 XPM913 B

Ac6MQrqM…93sko4N1 AY9F7Byy…EfAVw9Yf AVSRHCfX…pYML2Mhc APeshfYV…3PKcKMKH AMBbmvEz…yFqmSmw2

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.

1.058 × 10⁹⁷(98-digit number)

10585986195656157101…69934005530679189120

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

1.058 × 10⁹⁷(98-digit number)

10585986195656157101…69934005530679189119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.058 × 10⁹⁷(98-digit number)

10585986195656157101…69934005530679189121

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

2.117 × 10⁹⁷(98-digit number)

21171972391312314203…39868011061358378239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.117 × 10⁹⁷(98-digit number)

21171972391312314203…39868011061358378241

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

4.234 × 10⁹⁷(98-digit number)

42343944782624628407…79736022122716756479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.234 × 10⁹⁷(98-digit number)

42343944782624628407…79736022122716756481

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

8.468 × 10⁹⁷(98-digit number)

84687889565249256814…59472044245433512959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.468 × 10⁹⁷(98-digit number)

84687889565249256814…59472044245433512961

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

1.693 × 10⁹⁸(99-digit number)

16937577913049851362…18944088490867025919

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 275590

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 bad6d3783afe7ea59c68e50702d70c95f27f9d9e1297109dbb669309f208631c

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 #275,590 on Chainz ↗