Home/Chain Registry/Block #312,611

Block #312,611

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/15/2013, 2:35:04 AM · Difficulty 9.9959 · 6,481,576 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b5ac9386dfade58382fa3171046443251b58256be45ff2e0b37f0ed928f04d84

View on Chainz ↗

Height

#312,611

Difficulty

9.995865

Transactions

Size

206 B

Version

Bits

09fef10a

Nonce

154,959

Timestamp

12/15/2013, 2:35:04 AM

Confirmations

6,481,576

Merkle Root

b83e2f1a6f2563191c36ffe5714989e8f76b3b67ffc95133eaeb87ebc25a790a

Transactions (1)

Coinbaseb83e2f1a6f2563…eb87ebc25a790a

1 in → 1 out9.9900 XPM116 B

AbwWkWZt…kawDhufa

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.

5.400 × 10⁹⁴(95-digit number)

54000800799798587408…66263177460276385120

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

5.400 × 10⁹⁴(95-digit number)

54000800799798587408…66263177460276385119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.400 × 10⁹⁴(95-digit number)

54000800799798587408…66263177460276385121

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

1.080 × 10⁹⁵(96-digit number)

10800160159959717481…32526354920552770239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.080 × 10⁹⁵(96-digit number)

10800160159959717481…32526354920552770241

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

2.160 × 10⁹⁵(96-digit number)

21600320319919434963…65052709841105540479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.160 × 10⁹⁵(96-digit number)

21600320319919434963…65052709841105540481

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

4.320 × 10⁹⁵(96-digit number)

43200640639838869927…30105419682211080959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.320 × 10⁹⁵(96-digit number)

43200640639838869927…30105419682211080961

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

8.640 × 10⁹⁵(96-digit number)

86401281279677739854…60210839364422161919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.640 × 10⁹⁵(96-digit number)

86401281279677739854…60210839364422161921

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 312611

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 b5ac9386dfade58382fa3171046443251b58256be45ff2e0b37f0ed928f04d84

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 #312,611 on Chainz ↗