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Block #281,484

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/29/2013, 1:07:33 AM Β· Difficulty 9.9771 Β· 6,517,028 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
58a28e6cf54b0e6bc2e6e1f8e66c34872cf5da964929a5ca11780d0d5cc6bf29
View on Chainz β†—

Height

#281,484

Difficulty

9.977140

Transactions

1

Size

199 B

Version

2

Bits

09fa25d6

Nonce

186,941

Timestamp

11/29/2013, 1:07:33 AM

Confirmations

6,517,028

Merkle Root

16a6c679932267dd5ac989a48e5de66e4178b81d03e7ec2b82db830b82686149
Transactions (1)
Coinbase16a6c679932267…db830b82686149
1 in β†’ 1 out10.0300 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.

2.393 Γ— 10⁹¹(92-digit number)
23930924738281577234…89035323100039739430
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
2.393 Γ— 10⁹¹(92-digit number)
23930924738281577234…89035323100039739429
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.393 Γ— 10⁹¹(92-digit number)
23930924738281577234…89035323100039739431
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
4.786 Γ— 10⁹¹(92-digit number)
47861849476563154469…78070646200079478859
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.786 Γ— 10⁹¹(92-digit number)
47861849476563154469…78070646200079478861
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
9.572 Γ— 10⁹¹(92-digit number)
95723698953126308938…56141292400158957719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.572 Γ— 10⁹¹(92-digit number)
95723698953126308938…56141292400158957721
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
1.914 Γ— 10⁹²(93-digit number)
19144739790625261787…12282584800317915439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.914 Γ— 10⁹²(93-digit number)
19144739790625261787…12282584800317915441
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
3.828 Γ— 10⁹²(93-digit number)
38289479581250523575…24565169600635830879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.828 Γ— 10⁹²(93-digit number)
38289479581250523575…24565169600635830881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
7.657 Γ— 10⁹²(93-digit number)
76578959162501047150…49130339201271661759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 281484

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 58a28e6cf54b0e6bc2e6e1f8e66c34872cf5da964929a5ca11780d0d5cc6bf29

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 #281,484 on Chainz β†—
Circulating Supply:57,632,109 XPMΒ·at block #6,798,511 Β· updates every 60s
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