Home/Chain Registry/Block #488,216

Block #488,216

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/12/2014, 2:25:07 PM · Difficulty 10.6506 · 6,338,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a3c6ca130e9d855aea0a17a19fcc483f820c6072376140f5a77c98dcaae96f9c

View on Chainz ↗

Height

#488,216

Difficulty

10.650621

Transactions

Size

841 B

Version

Bits

0aa68f19

Nonce

13,645

Timestamp

4/12/2014, 2:25:07 PM

Confirmations

6,338,958

Merkle Root

57a990fe1718780e3c1744c82c971a59b94a322fb7716ab198738932597203ac

Transactions (3)

Coinbase5ec51d73e1dc6a…58fc61ff2fe597

1 in → 1 out8.8200 XPM116 B

AbwWkWZt…kawDhufa

ddce497ffe246e…b70ef26f3035a2

2 in → 5 out17.8000 XPM407 B

AWkTY9wW…HrBW1npq AHbu8w6V…13P7BwSQ AHXJ1dhk…mhL46N6m AeKNrjNj…1NEq95Ta AcBvLaSu…X3gaHvJ1

ef68c5e82b456d…fefb26786bd3ad

1 in → 2 out10.0239 XPM226 B

AJuott63…gcv3zzS5 ALxbXrs1…s2Ly78eU

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.

5.495 × 10⁹⁸(99-digit number)

54958653216863637139…28126251711942862080

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

5.495 × 10⁹⁸(99-digit number)

54958653216863637139…28126251711942862079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.495 × 10⁹⁸(99-digit number)

54958653216863637139…28126251711942862081

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

1.099 × 10⁹⁹(100-digit number)

10991730643372727427…56252503423885724159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.099 × 10⁹⁹(100-digit number)

10991730643372727427…56252503423885724161

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

2.198 × 10⁹⁹(100-digit number)

21983461286745454855…12505006847771448319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.198 × 10⁹⁹(100-digit number)

21983461286745454855…12505006847771448321

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

4.396 × 10⁹⁹(100-digit number)

43966922573490909711…25010013695542896639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.396 × 10⁹⁹(100-digit number)

43966922573490909711…25010013695542896641

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

8.793 × 10⁹⁹(100-digit number)

87933845146981819422…50020027391085793279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.793 × 10⁹⁹(100-digit number)

87933845146981819422…50020027391085793281

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 488216

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 a3c6ca130e9d855aea0a17a19fcc483f820c6072376140f5a77c98dcaae96f9c

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 #488,216 on Chainz ↗

Block #488,216

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