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Block #282,530

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2013, 10:20:25 AM Β· Difficulty 9.9793 Β· 6,531,649 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fb42f986ff6fe3c7bf834c04d80730d187a142c43754ad09f56ea949e8e1e536
View on Chainz β†—

Height

#282,530

Difficulty

9.979294

Transactions

1

Size

207 B

Version

2

Bits

09fab302

Nonce

9,797

Timestamp

11/29/2013, 10:20:25 AM

Confirmations

6,531,649

Merkle Root

b6f27c9fef06e1197d77361a50a3a9d934785b1f0231c2dbc1433b5fa1d21c14
Transactions (1)
Coinbaseb6f27c9fef06e1…433b5fa1d21c14
1 in β†’ 1 out10.0300 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.962 Γ— 10⁹⁢(97-digit number)
29625963529292321202…45310676392157285840
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
2.962 Γ— 10⁹⁢(97-digit number)
29625963529292321202…45310676392157285839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.962 Γ— 10⁹⁢(97-digit number)
29625963529292321202…45310676392157285841
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
5.925 Γ— 10⁹⁢(97-digit number)
59251927058584642405…90621352784314571679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.925 Γ— 10⁹⁢(97-digit number)
59251927058584642405…90621352784314571681
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
1.185 Γ— 10⁹⁷(98-digit number)
11850385411716928481…81242705568629143359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.185 Γ— 10⁹⁷(98-digit number)
11850385411716928481…81242705568629143361
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
2.370 Γ— 10⁹⁷(98-digit number)
23700770823433856962…62485411137258286719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.370 Γ— 10⁹⁷(98-digit number)
23700770823433856962…62485411137258286721
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
4.740 Γ— 10⁹⁷(98-digit number)
47401541646867713924…24970822274516573439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 282530

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 fb42f986ff6fe3c7bf834c04d80730d187a142c43754ad09f56ea949e8e1e536

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 #282,530 on Chainz β†—
Circulating Supply:57,757,504 XPMΒ·at block #6,814,178 Β· updates every 60s
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