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Block #466,990

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 12:14:59 PM · Difficulty 10.4312 · 6,360,376 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

65dc83f11bd78b6e17096fdf03e1213dce0bb0607e62aef83700d7c9e7efdd91

View on Chainz ↗

Height

#466,990

Difficulty

10.431173

Transactions

Size

881 B

Version

Bits

0a6e6157

Nonce

215,767

Timestamp

3/30/2014, 12:14:59 PM

Confirmations

6,360,376

Merkle Root

9dadd053208fd2c28948114ae69ee4eddcf9771da66842d9b54c700691b46e8d

Transactions (4)

Coinbasebed955057e1b8c…f198ba996365c3

1 in → 1 out9.2100 XPM110 B

AeKNrjNj…1NEq95Ta

4589b8c37165a9…e5d55fb8ae23d7

1 in → 2 out99.5609 XPM226 B

ALaXqtvM…gWaTZ4GY AdpQH7cM…7M1veJPq

e135d05d1df98d…1017cfca775e64

1 in → 2 out19.3193 XPM226 B

AbsM88Ay…WwVV3kDM ASM11XDD…Crd8pbyi

6a7c03e1ac9a5a…ee110f337b75a5

1 in → 2 out0.0913 XPM227 B

AHF8Uczf…eQmakkji AXLu6weF…RbHeFFJ8

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.

3.088 × 10⁹⁹(100-digit number)

30889589238184084346…16139460865023370240

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

3.088 × 10⁹⁹(100-digit number)

30889589238184084346…16139460865023370239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.088 × 10⁹⁹(100-digit number)

30889589238184084346…16139460865023370241

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

6.177 × 10⁹⁹(100-digit number)

61779178476368168692…32278921730046740479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.177 × 10⁹⁹(100-digit number)

61779178476368168692…32278921730046740481

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

1.235 × 10¹⁰⁰(101-digit number)

12355835695273633738…64557843460093480959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.235 × 10¹⁰⁰(101-digit number)

12355835695273633738…64557843460093480961

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

2.471 × 10¹⁰⁰(101-digit number)

24711671390547267477…29115686920186961919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.471 × 10¹⁰⁰(101-digit number)

24711671390547267477…29115686920186961921

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

4.942 × 10¹⁰⁰(101-digit number)

49423342781094534954…58231373840373923839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.942 × 10¹⁰⁰(101-digit number)

49423342781094534954…58231373840373923841

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 466990

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 65dc83f11bd78b6e17096fdf03e1213dce0bb0607e62aef83700d7c9e7efdd91

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 #466,990 on Chainz ↗

Block #466,990

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