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Home/Chain Registry/Block #3,010,198

Block #3,010,198

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/15/2019, 4:01:29 AM Β· Difficulty 11.2012 Β· 3,831,970 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
04f8facfe4a9a3df2f6c97fce891ee8f7624eec6f133788c8ff34a7c992b9b49
View on Chainz β†—

Difficulty

11.201240

Transactions

1

Size

201 B

Version

2

Bits

0b33847e

Nonce

224,761,657

Timestamp

1/15/2019, 4:01:29 AM

Confirmations

3,831,970

Merkle Root

679c473a628446903e14ad5e2b7af92c0c00c41194af9f18db891a9fb073c8e3
Transactions (1)
Coinbase679c473a628446…891a9fb073c8e3
1 in β†’ 1 out7.9600 XPM110 B
AbXwmGxD…4XXYP765
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.

2.794 Γ— 10⁹⁷(98-digit number)
27940125079598398940…61471253064336028160
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
2.794 Γ— 10⁹⁷(98-digit number)
27940125079598398940…61471253064336028159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.794 Γ— 10⁹⁷(98-digit number)
27940125079598398940…61471253064336028161
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
5.588 Γ— 10⁹⁷(98-digit number)
55880250159196797880…22942506128672056319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.588 Γ— 10⁹⁷(98-digit number)
55880250159196797880…22942506128672056321
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
1.117 Γ— 10⁹⁸(99-digit number)
11176050031839359576…45885012257344112639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.117 Γ— 10⁹⁸(99-digit number)
11176050031839359576…45885012257344112641
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
2.235 Γ— 10⁹⁸(99-digit number)
22352100063678719152…91770024514688225279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.235 Γ— 10⁹⁸(99-digit number)
22352100063678719152…91770024514688225281
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
4.470 Γ— 10⁹⁸(99-digit number)
44704200127357438304…83540049029376450559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.470 Γ— 10⁹⁸(99-digit number)
44704200127357438304…83540049029376450561
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
8.940 Γ— 10⁹⁸(99-digit number)
89408400254714876609…67080098058752901119
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 3010198

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 04f8facfe4a9a3df2f6c97fce891ee8f7624eec6f133788c8ff34a7c992b9b49

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 #3,010,198 on Chainz β†—
Circulating Supply:57,981,735 XPMΒ·at block #6,842,167 Β· updates every 60s
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