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Home/Chain Registry/Block #2,872,839

Block #2,872,839

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/8/2018, 4:58:16 PM Β· Difficulty 11.6648 Β· 3,970,619 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
04f0b5e255fab54fed6babc91c2b57c1d89224db5afc5f80d59e404c3239e6dd
View on Chainz β†—

Difficulty

11.664751

Transactions

1

Size

202 B

Version

2

Bits

0baa2d27

Nonce

1,179,534,759

Timestamp

10/8/2018, 4:58:16 PM

Confirmations

3,970,619

Merkle Root

d571ce53c3db74950fb489f96d267d1ef936c0a91ce6b0dbf770dc0c582519ec
Transactions (1)
Coinbased571ce53c3db74…70dc0c582519ec
1 in β†’ 1 out7.3400 XPM110 B
AZ8mbHED…NZLjnTke
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.

1.165 Γ— 10¹⁰⁰(101-digit number)
11652609297817626477…13834369642999971840
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
1.165 Γ— 10¹⁰⁰(101-digit number)
11652609297817626477…13834369642999971839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.165 Γ— 10¹⁰⁰(101-digit number)
11652609297817626477…13834369642999971841
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
2.330 Γ— 10¹⁰⁰(101-digit number)
23305218595635252955…27668739285999943679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.330 Γ— 10¹⁰⁰(101-digit number)
23305218595635252955…27668739285999943681
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
4.661 Γ— 10¹⁰⁰(101-digit number)
46610437191270505910…55337478571999887359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.661 Γ— 10¹⁰⁰(101-digit number)
46610437191270505910…55337478571999887361
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
9.322 Γ— 10¹⁰⁰(101-digit number)
93220874382541011821…10674957143999774719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.322 Γ— 10¹⁰⁰(101-digit number)
93220874382541011821…10674957143999774721
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
1.864 Γ— 10¹⁰¹(102-digit number)
18644174876508202364…21349914287999549439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.864 Γ— 10¹⁰¹(102-digit number)
18644174876508202364…21349914287999549441
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
3.728 Γ— 10¹⁰¹(102-digit number)
37288349753016404728…42699828575999098879
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 2872839

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 04f0b5e255fab54fed6babc91c2b57c1d89224db5afc5f80d59e404c3239e6dd

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 #2,872,839 on Chainz β†—
Circulating Supply:57,992,032 XPMΒ·at block #6,843,457 Β· updates every 60s
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