Home/Chain Registry/Block #259,538

Block #259,538

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/13/2013, 4:35:48 PM · Difficulty 9.9774 · 6,565,987 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

55ab41fb7fa0380c4d7ec60ce17b857e1dc108ccc49faf183027bf7464fcc87a

View on Chainz ↗

Height

#259,538

Difficulty

9.977381

Transactions

Size

949 B

Version

Bits

09fa35aa

Nonce

14,220

Timestamp

11/13/2013, 4:35:48 PM

Confirmations

6,565,987

Merkle Root

1438e620283065e79d46844710642e98599804c6d8816bd8b68ff0b21efc1a31

Transactions (3)

Coinbaseaf302a0ac455e6…62a208ec5bdd13

1 in → 2 out10.0500 XPM141 B

AKcbk49N…GJbKa7j1 Abiw8n3q…ZnZfgvQW

b444d5efab84d5…3e8cdfa8a790ee

3 in → 1 out104.2359 XPM490 B

ATknEwpv…tz6xvy1e

7f35184e3c4a28…e01b00dd552049

1 in → 2 out2.0954 XPM227 B

ANHbaxZp…XjnHCJJs AGf3DcCg…TcaqBqaB

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.

1.182 × 10⁹⁷(98-digit number)

11825129971137614683…54617316310961541120

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

1.182 × 10⁹⁷(98-digit number)

11825129971137614683…54617316310961541119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.182 × 10⁹⁷(98-digit number)

11825129971137614683…54617316310961541121

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

2.365 × 10⁹⁷(98-digit number)

23650259942275229367…09234632621923082239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.365 × 10⁹⁷(98-digit number)

23650259942275229367…09234632621923082241

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

4.730 × 10⁹⁷(98-digit number)

47300519884550458734…18469265243846164479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.730 × 10⁹⁷(98-digit number)

47300519884550458734…18469265243846164481

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

9.460 × 10⁹⁷(98-digit number)

94601039769100917469…36938530487692328959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.460 × 10⁹⁷(98-digit number)

94601039769100917469…36938530487692328961

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

1.892 × 10⁹⁸(99-digit number)

18920207953820183493…73877060975384657919

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 259538

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 55ab41fb7fa0380c4d7ec60ce17b857e1dc108ccc49faf183027bf7464fcc87a

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 #259,538 on Chainz ↗

Block #259,538

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