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Block #243,938

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2013, 2:03:40 PM Β· Difficulty 9.9622 Β· 6,588,927 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
49cede7a25e7253f15be256a057edfb3cb83da63fb9d7d608835b1e09ac6d5e4
View on Chainz β†—

Height

#243,938

Difficulty

9.962245

Transactions

1

Size

205 B

Version

2

Bits

09f655b0

Nonce

1,149

Timestamp

11/4/2013, 2:03:40 PM

Confirmations

6,588,927

Merkle Root

52f8e8eb64ab0472f06a3d2b06b1e642a59ce3303789c2edc719c159e55ef9ed
Transactions (1)
Coinbase52f8e8eb64ab04…19c159e55ef9ed
1 in β†’ 1 out10.0600 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.

4.281 Γ— 10⁹¹(92-digit number)
42814864310372895560…88748193819999479800
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
4.281 Γ— 10⁹¹(92-digit number)
42814864310372895560…88748193819999479799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.281 Γ— 10⁹¹(92-digit number)
42814864310372895560…88748193819999479801
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
8.562 Γ— 10⁹¹(92-digit number)
85629728620745791120…77496387639998959599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.562 Γ— 10⁹¹(92-digit number)
85629728620745791120…77496387639998959601
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
1.712 Γ— 10⁹²(93-digit number)
17125945724149158224…54992775279997919199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.712 Γ— 10⁹²(93-digit number)
17125945724149158224…54992775279997919201
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
3.425 Γ— 10⁹²(93-digit number)
34251891448298316448…09985550559995838399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.425 Γ— 10⁹²(93-digit number)
34251891448298316448…09985550559995838401
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
6.850 Γ— 10⁹²(93-digit number)
68503782896596632896…19971101119991676799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.850 Γ— 10⁹²(93-digit number)
68503782896596632896…19971101119991676801
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 243938

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 49cede7a25e7253f15be256a057edfb3cb83da63fb9d7d608835b1e09ac6d5e4

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 #243,938 on Chainz β†—
Circulating Supply:57,907,087 XPMΒ·at block #6,832,864 Β· updates every 60s
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