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Home/Chain Registry/Block #1,183,170

Block #1,183,170

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2015, 3:23:33 AM Β· Difficulty 10.9071 Β· 5,643,076 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f0171c09651d128261d212b08135594631708f9dbe69b76020d14ac8445fa182
View on Chainz β†—

Difficulty

10.907074

Transactions

1

Size

200 B

Version

2

Bits

0ae835f9

Nonce

304,773,203

Timestamp

8/5/2015, 3:23:33 AM

Confirmations

5,643,076

Merkle Root

7d6049290f18b7699a4e20c7a21e1dc66e93deec1bf69097d5f57e053ee423cf
Transactions (1)
Coinbase7d6049290f18b7…f57e053ee423cf
1 in β†’ 1 out8.3900 XPM110 B
AYQwtczW…2TRn6xSh
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.

2.290 Γ— 10⁹⁴(95-digit number)
22903737184498461916…30204593362089779200
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
2.290 Γ— 10⁹⁴(95-digit number)
22903737184498461916…30204593362089779199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.290 Γ— 10⁹⁴(95-digit number)
22903737184498461916…30204593362089779201
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
4.580 Γ— 10⁹⁴(95-digit number)
45807474368996923832…60409186724179558399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.580 Γ— 10⁹⁴(95-digit number)
45807474368996923832…60409186724179558401
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
9.161 Γ— 10⁹⁴(95-digit number)
91614948737993847665…20818373448359116799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.161 Γ— 10⁹⁴(95-digit number)
91614948737993847665…20818373448359116801
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
1.832 Γ— 10⁹⁡(96-digit number)
18322989747598769533…41636746896718233599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.832 Γ— 10⁹⁡(96-digit number)
18322989747598769533…41636746896718233601
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
3.664 Γ— 10⁹⁡(96-digit number)
36645979495197539066…83273493793436467199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.664 Γ— 10⁹⁡(96-digit number)
36645979495197539066…83273493793436467201
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
7.329 Γ— 10⁹⁡(96-digit number)
73291958990395078132…66546987586872934399
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 1183170

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 f0171c09651d128261d212b08135594631708f9dbe69b76020d14ac8445fa182

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 #1,183,170 on Chainz β†—
Circulating Supply:57,854,101 XPMΒ·at block #6,826,245 Β· updates every 60s
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