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Block #282,896

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2013, 1:20:44 PM Β· Difficulty 9.9801 Β· 6,544,419 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
73e6d3f0e316fe599c1ffdfd72d454d4503dff33d2307eef43aa24e5a50e515d
View on Chainz β†—

Height

#282,896

Difficulty

9.980054

Transactions

1

Size

207 B

Version

2

Bits

09fae4d5

Nonce

5,244

Timestamp

11/29/2013, 1:20:44 PM

Confirmations

6,544,419

Merkle Root

eb9ef422963c4bc9c635f4141871f5e0ddcaa0f6c5913ec252d5c80b3c11a902
Transactions (1)
Coinbaseeb9ef422963c4b…d5c80b3c11a902
1 in β†’ 1 out10.0200 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.

1.367 Γ— 10⁹⁸(99-digit number)
13671277043414585327…71114706239919289000
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
1.367 Γ— 10⁹⁸(99-digit number)
13671277043414585327…71114706239919288999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.367 Γ— 10⁹⁸(99-digit number)
13671277043414585327…71114706239919289001
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
2.734 Γ— 10⁹⁸(99-digit number)
27342554086829170654…42229412479838577999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.734 Γ— 10⁹⁸(99-digit number)
27342554086829170654…42229412479838578001
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
5.468 Γ— 10⁹⁸(99-digit number)
54685108173658341309…84458824959677155999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.468 Γ— 10⁹⁸(99-digit number)
54685108173658341309…84458824959677156001
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
1.093 Γ— 10⁹⁹(100-digit number)
10937021634731668261…68917649919354311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.093 Γ— 10⁹⁹(100-digit number)
10937021634731668261…68917649919354312001
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
2.187 Γ— 10⁹⁹(100-digit number)
21874043269463336523…37835299838708623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.187 Γ— 10⁹⁹(100-digit number)
21874043269463336523…37835299838708624001
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 282896

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 73e6d3f0e316fe599c1ffdfd72d454d4503dff33d2307eef43aa24e5a50e515d

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 #282,896 on Chainz β†—
Circulating Supply:57,862,632 XPMΒ·at block #6,827,314 Β· updates every 60s
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