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Home/Chain Registry/Block #2,232,813

Block #2,232,813

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/1/2017, 9:13:31 PM Β· Difficulty 10.9461 Β· 4,606,474 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8ec1f96f5062024a727a028e62535430f2c738bc73553e3ce752e56673d9cc77
View on Chainz β†—

Difficulty

10.946069

Transactions

1

Size

200 B

Version

2

Bits

0af23199

Nonce

1,537,019,526

Timestamp

8/1/2017, 9:13:31 PM

Confirmations

4,606,474

Merkle Root

1f49ed24729564fd916fbfadd899c07225687ec0e96a2855cbb588862ce598fd
Transactions (1)
Coinbase1f49ed24729564…b588862ce598fd
1 in β†’ 1 out8.3300 XPM110 B
APzgQjhA…rzt4vPcc
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.

9.592 Γ— 10⁹³(94-digit number)
95924480972816094346…56176610991506651280
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
9.592 Γ— 10⁹³(94-digit number)
95924480972816094346…56176610991506651279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.592 Γ— 10⁹³(94-digit number)
95924480972816094346…56176610991506651281
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
1.918 Γ— 10⁹⁴(95-digit number)
19184896194563218869…12353221983013302559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.918 Γ— 10⁹⁴(95-digit number)
19184896194563218869…12353221983013302561
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
3.836 Γ— 10⁹⁴(95-digit number)
38369792389126437738…24706443966026605119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.836 Γ— 10⁹⁴(95-digit number)
38369792389126437738…24706443966026605121
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
7.673 Γ— 10⁹⁴(95-digit number)
76739584778252875476…49412887932053210239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.673 Γ— 10⁹⁴(95-digit number)
76739584778252875476…49412887932053210241
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
1.534 Γ— 10⁹⁡(96-digit number)
15347916955650575095…98825775864106420479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.534 Γ— 10⁹⁡(96-digit number)
15347916955650575095…98825775864106420481
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 2232813

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 8ec1f96f5062024a727a028e62535430f2c738bc73553e3ce752e56673d9cc77

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 #2,232,813 on Chainz β†—
Circulating Supply:57,958,583 XPMΒ·at block #6,839,286 Β· updates every 60s
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