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Block #510,723

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/25/2014, 8:04:34 PM Β· Difficulty 10.8264 Β· 6,285,874 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0f4b31f82a3316d4b5a04e0914a7fe0c00a1837de82dd313deef3abe8f882c47
View on Chainz β†—

Height

#510,723

Difficulty

10.826437

Transactions

1

Size

223 B

Version

2

Bits

0ad39168

Nonce

673,513

Timestamp

4/25/2014, 8:04:34 PM

Confirmations

6,285,874

Merkle Root

532eb095a992739b09cb1b24811d9263cb0f25ad4568466ef777898f46778d36
Transactions (1)
Coinbase532eb095a99273…77898f46778d36
1 in β†’ 2 out8.5200 XPM131 B
AMVf7Jrg…xd5AVR7CAJno7LX2…vo4wdWtY
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.

1.354 Γ— 10⁹⁹(100-digit number)
13543023806003408254…94589677009570931200
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
1.354 Γ— 10⁹⁹(100-digit number)
13543023806003408254…94589677009570931199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.354 Γ— 10⁹⁹(100-digit number)
13543023806003408254…94589677009570931201
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
2.708 Γ— 10⁹⁹(100-digit number)
27086047612006816508…89179354019141862399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.708 Γ— 10⁹⁹(100-digit number)
27086047612006816508…89179354019141862401
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
5.417 Γ— 10⁹⁹(100-digit number)
54172095224013633017…78358708038283724799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.417 Γ— 10⁹⁹(100-digit number)
54172095224013633017…78358708038283724801
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
1.083 Γ— 10¹⁰⁰(101-digit number)
10834419044802726603…56717416076567449599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10¹⁰⁰(101-digit number)
10834419044802726603…56717416076567449601
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
2.166 Γ— 10¹⁰⁰(101-digit number)
21668838089605453207…13434832153134899199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.166 Γ— 10¹⁰⁰(101-digit number)
21668838089605453207…13434832153134899201
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 510723

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 0f4b31f82a3316d4b5a04e0914a7fe0c00a1837de82dd313deef3abe8f882c47

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 #510,723 on Chainz β†—
Circulating Supply:57,616,779 XPMΒ·at block #6,796,596 Β· updates every 60s
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