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Home/Chain Registry/Block #3,321,278

Block #3,321,278

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/21/2019, 10:13:32 PM Β· Difficulty 11.0210 Β· 3,505,679 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1f320a8c00132f17b1e1d3f695b5332cfd818fedcf94fd19c52131ade9188f67
View on Chainz β†—

Difficulty

11.021010

Transactions

1

Size

200 B

Version

2

Bits

0b0560f0

Nonce

320,520,424

Timestamp

8/21/2019, 10:13:32 PM

Confirmations

3,505,679

Merkle Root

62b04bac66c3bb70212b26bf5ee118f2ede826bf7594ae4ba5ba23abd3a0d441
Transactions (1)
Coinbase62b04bac66c3bb…ba23abd3a0d441
1 in β†’ 1 out8.2200 XPM110 B
AXfJqzUb…HXeXmjMz
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.

1.075 Γ— 10⁹⁡(96-digit number)
10758182105540715732…34844489391536152000
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
1.075 Γ— 10⁹⁡(96-digit number)
10758182105540715732…34844489391536151999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.075 Γ— 10⁹⁡(96-digit number)
10758182105540715732…34844489391536152001
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
2.151 Γ— 10⁹⁡(96-digit number)
21516364211081431465…69688978783072303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.151 Γ— 10⁹⁡(96-digit number)
21516364211081431465…69688978783072304001
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
4.303 Γ— 10⁹⁡(96-digit number)
43032728422162862931…39377957566144607999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.303 Γ— 10⁹⁡(96-digit number)
43032728422162862931…39377957566144608001
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
8.606 Γ— 10⁹⁡(96-digit number)
86065456844325725862…78755915132289215999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.606 Γ— 10⁹⁡(96-digit number)
86065456844325725862…78755915132289216001
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
1.721 Γ— 10⁹⁢(97-digit number)
17213091368865145172…57511830264578431999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.721 Γ— 10⁹⁢(97-digit number)
17213091368865145172…57511830264578432001
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
3.442 Γ— 10⁹⁢(97-digit number)
34426182737730290344…15023660529156863999
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 3321278

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 1f320a8c00132f17b1e1d3f695b5332cfd818fedcf94fd19c52131ade9188f67

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 #3,321,278 on Chainz β†—
Circulating Supply:57,859,831 XPMΒ·at block #6,826,956 Β· updates every 60s
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