Home/Chain Registry/Block #303,649

Block #303,649

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/10/2013, 12:09:16 PM · Difficulty 9.9931 · 6,520,902 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf8187a8b3ac8b9dafa8d85d8388fddbb827873faf5b3c7325769ee6cf377847

View on Chainz ↗

Height

#303,649

Difficulty

9.993072

Transactions

Size

209 B

Version

Bits

09fe39fc

Nonce

12,497

Timestamp

12/10/2013, 12:09:16 PM

Confirmations

6,520,902

Merkle Root

4e4f2fe8031396c8b6d97d373a7c6e534e03c4a4c31c3beea0b63faffcd56415

Transactions (1)

Coinbase4e4f2fe8031396…b63faffcd56415

1 in → 1 out10.0000 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.

9.408 × 10¹⁰⁰(101-digit number)

94083155504840530244…43360528033006551040

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

9.408 × 10¹⁰⁰(101-digit number)

94083155504840530244…43360528033006551039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.408 × 10¹⁰⁰(101-digit number)

94083155504840530244…43360528033006551041

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

1.881 × 10¹⁰¹(102-digit number)

18816631100968106048…86721056066013102079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.881 × 10¹⁰¹(102-digit number)

18816631100968106048…86721056066013102081

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

3.763 × 10¹⁰¹(102-digit number)

37633262201936212097…73442112132026204159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.763 × 10¹⁰¹(102-digit number)

37633262201936212097…73442112132026204161

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

7.526 × 10¹⁰¹(102-digit number)

75266524403872424195…46884224264052408319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.526 × 10¹⁰¹(102-digit number)

75266524403872424195…46884224264052408321

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

1.505 × 10¹⁰²(103-digit number)

15053304880774484839…93768448528104816639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.505 × 10¹⁰²(103-digit number)

15053304880774484839…93768448528104816641

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 303649

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 cf8187a8b3ac8b9dafa8d85d8388fddbb827873faf5b3c7325769ee6cf377847

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 #303,649 on Chainz ↗

Block #303,649

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