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Block #464,828

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/29/2014, 1:20:17 AM Β· Difficulty 10.4230 Β· 6,347,830 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5db7ba1b7cb5b9148fa2e7a9c6c5139639fb3daef500d3bee27585695cae857b
View on Chainz β†—

Height

#464,828

Difficulty

10.422963

Transactions

1

Size

200 B

Version

2

Bits

0a6c4753

Nonce

672,452

Timestamp

3/29/2014, 1:20:17 AM

Confirmations

6,347,830

Merkle Root

1f51f2b76a3b2fcb68ace6df7744e8dba97549e39202b0bbac45a36a9a530baf
Transactions (1)
Coinbase1f51f2b76a3b2f…45a36a9a530baf
1 in β†’ 1 out9.1900 XPM110 B
AeKNrjNj…1NEq95Ta
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.921 Γ— 10⁹⁴(95-digit number)
29215991490744386084…97059769631913239260
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.921 Γ— 10⁹⁴(95-digit number)
29215991490744386084…97059769631913239259
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.921 Γ— 10⁹⁴(95-digit number)
29215991490744386084…97059769631913239261
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
5.843 Γ— 10⁹⁴(95-digit number)
58431982981488772169…94119539263826478519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.843 Γ— 10⁹⁴(95-digit number)
58431982981488772169…94119539263826478521
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
1.168 Γ— 10⁹⁡(96-digit number)
11686396596297754433…88239078527652957039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.168 Γ— 10⁹⁡(96-digit number)
11686396596297754433…88239078527652957041
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
2.337 Γ— 10⁹⁡(96-digit number)
23372793192595508867…76478157055305914079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.337 Γ— 10⁹⁡(96-digit number)
23372793192595508867…76478157055305914081
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
4.674 Γ— 10⁹⁡(96-digit number)
46745586385191017735…52956314110611828159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.674 Γ— 10⁹⁡(96-digit number)
46745586385191017735…52956314110611828161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 464828

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 5db7ba1b7cb5b9148fa2e7a9c6c5139639fb3daef500d3bee27585695cae857b

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 β†’ Debug Window β†’ 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 #464,828 on Chainz β†—
Circulating Supply:57,745,294 XPMΒ·at block #6,812,657 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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