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Block #3,171,203

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/6/2019, 10:35:46 PM Β· Difficulty 11.3101 Β· 3,655,525 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2af3ee8cc684469a9c554300cdedeba2e8871461a4c1863d39dc26c1a8acdf08
View on Chainz β†—

Difficulty

11.310063

Transactions

1

Size

201 B

Version

2

Bits

0b4f6047

Nonce

334,050,848

Timestamp

5/6/2019, 10:35:46 PM

Confirmations

3,655,525

Merkle Root

72ed70079f15afba2484d50a7ff635014bec5bee78641c82e704e5595d0135a4
Transactions (1)
Coinbase72ed70079f15af…04e5595d0135a4
1 in β†’ 1 out7.8000 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.

2.929 Γ— 10⁹⁢(97-digit number)
29293483139142911115…70369177377583104000
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
2.929 Γ— 10⁹⁢(97-digit number)
29293483139142911115…70369177377583103999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.929 Γ— 10⁹⁢(97-digit number)
29293483139142911115…70369177377583104001
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
5.858 Γ— 10⁹⁢(97-digit number)
58586966278285822231…40738354755166207999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.858 Γ— 10⁹⁢(97-digit number)
58586966278285822231…40738354755166208001
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
1.171 Γ— 10⁹⁷(98-digit number)
11717393255657164446…81476709510332415999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.171 Γ— 10⁹⁷(98-digit number)
11717393255657164446…81476709510332416001
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
2.343 Γ— 10⁹⁷(98-digit number)
23434786511314328892…62953419020664831999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.343 Γ— 10⁹⁷(98-digit number)
23434786511314328892…62953419020664832001
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
4.686 Γ— 10⁹⁷(98-digit number)
46869573022628657785…25906838041329663999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.686 Γ— 10⁹⁷(98-digit number)
46869573022628657785…25906838041329664001
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
9.373 Γ— 10⁹⁷(98-digit number)
93739146045257315570…51813676082659327999
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 3171203

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 2af3ee8cc684469a9c554300cdedeba2e8871461a4c1863d39dc26c1a8acdf08

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 #3,171,203 on Chainz β†—
Circulating Supply:57,857,977 XPMΒ·at block #6,826,727 Β· updates every 60s
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