Home/Chain Registry/Block #315,285

Block #315,285

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/16/2013, 10:36:22 AM · Difficulty 10.0935 · 6,509,276 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2b4c9c1e0aa2a32cf053df86a009ca6b260202739d5f22c89517e18aeffd85d

View on Chainz ↗

Height

#315,285

Difficulty

10.093460

Transactions

Size

208 B

Version

Bits

0a17ed02

Nonce

422,450

Timestamp

12/16/2013, 10:36:22 AM

Confirmations

6,509,276

Merkle Root

5a16da31e266229bbcb08011a76681c00c6ae08c91fce8a80782888caee9aec6

Transactions (1)

Coinbase5a16da31e26622…82888caee9aec6

1 in → 1 out9.8000 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.

2.439 × 10¹⁰⁰(101-digit number)

24397245287260253072…44410166867108768000

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

2.439 × 10¹⁰⁰(101-digit number)

24397245287260253072…44410166867108767999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.439 × 10¹⁰⁰(101-digit number)

24397245287260253072…44410166867108768001

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

4.879 × 10¹⁰⁰(101-digit number)

48794490574520506145…88820333734217535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.879 × 10¹⁰⁰(101-digit number)

48794490574520506145…88820333734217536001

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

9.758 × 10¹⁰⁰(101-digit number)

97588981149041012291…77640667468435071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.758 × 10¹⁰⁰(101-digit number)

97588981149041012291…77640667468435072001

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

1.951 × 10¹⁰¹(102-digit number)

19517796229808202458…55281334936870143999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.951 × 10¹⁰¹(102-digit number)

19517796229808202458…55281334936870144001

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

3.903 × 10¹⁰¹(102-digit number)

39035592459616404916…10562669873740287999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.903 × 10¹⁰¹(102-digit number)

39035592459616404916…10562669873740288001

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 315285

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 d2b4c9c1e0aa2a32cf053df86a009ca6b260202739d5f22c89517e18aeffd85d

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 #315,285 on Chainz ↗

Block #315,285

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