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Block #243,276

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/4/2013, 5:07:35 AM Β· Difficulty 9.9614 Β· 6,593,513 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0fe35c251c36282754a731cacd60ab8904225a69b8410046966fb92fca9fdd45
View on Chainz β†—

Height

#243,276

Difficulty

9.961385

Transactions

1

Size

200 B

Version

2

Bits

09f61d57

Nonce

514,599

Timestamp

11/4/2013, 5:07:35 AM

Confirmations

6,593,513

Merkle Root

83dda913b47ed3ff49f5a604462cf7520269ba7a2ebced5266773f89c4bd4483
Transactions (1)
Coinbase83dda913b47ed3…773f89c4bd4483
1 in β†’ 1 out10.0600 XPM109 B
AeTn9Y6x…cP9uukU7
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.

4.877 Γ— 10⁹⁢(97-digit number)
48776915071200071899…42814301909685630400
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
4.877 Γ— 10⁹⁢(97-digit number)
48776915071200071899…42814301909685630399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.877 Γ— 10⁹⁢(97-digit number)
48776915071200071899…42814301909685630401
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
9.755 Γ— 10⁹⁢(97-digit number)
97553830142400143798…85628603819371260799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.755 Γ— 10⁹⁢(97-digit number)
97553830142400143798…85628603819371260801
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
1.951 Γ— 10⁹⁷(98-digit number)
19510766028480028759…71257207638742521599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.951 Γ— 10⁹⁷(98-digit number)
19510766028480028759…71257207638742521601
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
3.902 Γ— 10⁹⁷(98-digit number)
39021532056960057519…42514415277485043199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.902 Γ— 10⁹⁷(98-digit number)
39021532056960057519…42514415277485043201
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
7.804 Γ— 10⁹⁷(98-digit number)
78043064113920115039…85028830554970086399
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 243276

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 0fe35c251c36282754a731cacd60ab8904225a69b8410046966fb92fca9fdd45

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 #243,276 on Chainz β†—
Circulating Supply:57,938,592 XPMΒ·at block #6,836,788 Β· updates every 60s
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