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Block #244,653

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/5/2013, 12:13:30 AM Β· Difficulty 9.9631 Β· 6,555,678 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8a93304c9763fc6220d5bdeff032a7770fb9fca8ca7e329faf04e82366043e4c
View on Chainz β†—

Height

#244,653

Difficulty

9.963061

Transactions

1

Size

206 B

Version

2

Bits

09f68b2d

Nonce

7,754

Timestamp

11/5/2013, 12:13:30 AM

Confirmations

6,555,678

Merkle Root

be6a269c64eef3df293c3d6961cf0b3d752aba09cf78fc3cf4f941cc8b8a3423
Transactions (1)
Coinbasebe6a269c64eef3…f941cc8b8a3423
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.

3.083 Γ— 10⁹⁴(95-digit number)
30831036294642362201…29424728037069029120
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
3.083 Γ— 10⁹⁴(95-digit number)
30831036294642362201…29424728037069029119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.083 Γ— 10⁹⁴(95-digit number)
30831036294642362201…29424728037069029121
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
6.166 Γ— 10⁹⁴(95-digit number)
61662072589284724403…58849456074138058239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.166 Γ— 10⁹⁴(95-digit number)
61662072589284724403…58849456074138058241
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
1.233 Γ— 10⁹⁡(96-digit number)
12332414517856944880…17698912148276116479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.233 Γ— 10⁹⁡(96-digit number)
12332414517856944880…17698912148276116481
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
2.466 Γ— 10⁹⁡(96-digit number)
24664829035713889761…35397824296552232959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.466 Γ— 10⁹⁡(96-digit number)
24664829035713889761…35397824296552232961
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
4.932 Γ— 10⁹⁡(96-digit number)
49329658071427779522…70795648593104465919
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 244653

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 8a93304c9763fc6220d5bdeff032a7770fb9fca8ca7e329faf04e82366043e4c

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 #244,653 on Chainz β†—
Circulating Supply:57,646,705 XPMΒ·at block #6,800,330 Β· updates every 60s
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