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Block #249,832

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/8/2013, 4:28:23 AM Β· Difficulty 9.9674 Β· 6,587,931 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ac43ee60d55155f6ed3a60382a614adf887a3756c6bf497ed1bfa3a4927d3748
View on Chainz β†—

Height

#249,832

Difficulty

9.967423

Transactions

1

Size

207 B

Version

2

Bits

09f7a901

Nonce

343,112

Timestamp

11/8/2013, 4:28:23 AM

Confirmations

6,587,931

Merkle Root

1de2e37b18516a1f9d7bc2e664e10f8497b141733e9abd7771f2beb72dd04357
Transactions (1)
Coinbase1de2e37b18516a…f2beb72dd04357
1 in β†’ 1 out10.0500 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.

4.581 Γ— 10⁹⁷(98-digit number)
45818302246462876766…99509629406294592640
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
4.581 Γ— 10⁹⁷(98-digit number)
45818302246462876766…99509629406294592639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.581 Γ— 10⁹⁷(98-digit number)
45818302246462876766…99509629406294592641
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
9.163 Γ— 10⁹⁷(98-digit number)
91636604492925753532…99019258812589185279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.163 Γ— 10⁹⁷(98-digit number)
91636604492925753532…99019258812589185281
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
1.832 Γ— 10⁹⁸(99-digit number)
18327320898585150706…98038517625178370559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.832 Γ— 10⁹⁸(99-digit number)
18327320898585150706…98038517625178370561
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
3.665 Γ— 10⁹⁸(99-digit number)
36654641797170301413…96077035250356741119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.665 Γ— 10⁹⁸(99-digit number)
36654641797170301413…96077035250356741121
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
7.330 Γ— 10⁹⁸(99-digit number)
73309283594340602826…92154070500713482239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.330 Γ— 10⁹⁸(99-digit number)
73309283594340602826…92154070500713482241
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 249832

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 ac43ee60d55155f6ed3a60382a614adf887a3756c6bf497ed1bfa3a4927d3748

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 #249,832 on Chainz β†—
Circulating Supply:57,946,437 XPMΒ·at block #6,837,762 Β· updates every 60s
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