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Home/Chain Registry/Block #3,011,142

Block #3,011,142

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/15/2019, 7:48:51 PM Β· Difficulty 11.2006 Β· 3,831,502 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c7484f10942186f4ccadf0d337b822be7c91e5b525e1e4853b18b7e7324e14ba
View on Chainz β†—

Difficulty

11.200633

Transactions

1

Size

201 B

Version

2

Bits

0b335cae

Nonce

196,127,965

Timestamp

1/15/2019, 7:48:51 PM

Confirmations

3,831,502

Merkle Root

741ceeef675a28ed4af932de5f78ec61c02b7a7eecae4d9d66a29d9a02f6d31a
Transactions (1)
Coinbase741ceeef675a28…a29d9a02f6d31a
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.

1.680 Γ— 10⁹⁷(98-digit number)
16801353036630586409…84865301393650483200
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
1.680 Γ— 10⁹⁷(98-digit number)
16801353036630586409…84865301393650483199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.680 Γ— 10⁹⁷(98-digit number)
16801353036630586409…84865301393650483201
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
3.360 Γ— 10⁹⁷(98-digit number)
33602706073261172818…69730602787300966399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.360 Γ— 10⁹⁷(98-digit number)
33602706073261172818…69730602787300966401
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
6.720 Γ— 10⁹⁷(98-digit number)
67205412146522345637…39461205574601932799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.720 Γ— 10⁹⁷(98-digit number)
67205412146522345637…39461205574601932801
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
1.344 Γ— 10⁹⁸(99-digit number)
13441082429304469127…78922411149203865599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.344 Γ— 10⁹⁸(99-digit number)
13441082429304469127…78922411149203865601
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
2.688 Γ— 10⁹⁸(99-digit number)
26882164858608938254…57844822298407731199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.688 Γ— 10⁹⁸(99-digit number)
26882164858608938254…57844822298407731201
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
5.376 Γ— 10⁹⁸(99-digit number)
53764329717217876509…15689644596815462399
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 3011142

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 c7484f10942186f4ccadf0d337b822be7c91e5b525e1e4853b18b7e7324e14ba

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 #3,011,142 on Chainz β†—
Circulating Supply:57,985,586 XPMΒ·at block #6,842,643 Β· updates every 60s
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