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Home/Chain Registry/Block #3,186,342

Block #3,186,342

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/17/2019, 6:50:46 PM Β· Difficulty 11.2422 Β· 3,654,752 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2c88bd178db63a774997487a4d2126149ddd45c7187057549bfeb0dac563c3c
View on Chainz β†—

Difficulty

11.242173

Transactions

1

Size

200 B

Version

2

Bits

0b3dff0b

Nonce

576,342,535

Timestamp

5/17/2019, 6:50:46 PM

Confirmations

3,654,752

Merkle Root

d36771335ad5c42eed3bafae1a1b4140890f85117a1b40988caf6dfdb24c13e8
Transactions (1)
Coinbased36771335ad5c4…af6dfdb24c13e8
1 in β†’ 1 out7.9000 XPM109 B
AUMQRepm…tAfKmdW1
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.

4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979200
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
4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.289 Γ— 10⁹⁢(97-digit number)
42893743848802926755…41331975265628979201
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
8.578 Γ— 10⁹⁢(97-digit number)
85787487697605853511…82663950531257958399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.578 Γ— 10⁹⁢(97-digit number)
85787487697605853511…82663950531257958401
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
1.715 Γ— 10⁹⁷(98-digit number)
17157497539521170702…65327901062515916799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.715 Γ— 10⁹⁷(98-digit number)
17157497539521170702…65327901062515916801
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
3.431 Γ— 10⁹⁷(98-digit number)
34314995079042341404…30655802125031833599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.431 Γ— 10⁹⁷(98-digit number)
34314995079042341404…30655802125031833601
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
6.862 Γ— 10⁹⁷(98-digit number)
68629990158084682809…61311604250063667199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.862 Γ— 10⁹⁷(98-digit number)
68629990158084682809…61311604250063667201
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
1.372 Γ— 10⁹⁸(99-digit number)
13725998031616936561…22623208500127334399
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 3186342

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 e2c88bd178db63a774997487a4d2126149ddd45c7187057549bfeb0dac563c3c

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 #3,186,342 on Chainz β†—
Circulating Supply:57,973,117 XPMΒ·at block #6,841,093 Β· updates every 60s
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