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Home/Chain Registry/Block #1,390,826

Block #1,390,826

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/30/2015, 12:45:43 AM Β· Difficulty 10.8079 Β· 5,452,419 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c3a504057fb2e0bb2088549d602befca8b3890ce1a3732be1b1c5f9a53760bb2
View on Chainz β†—

Difficulty

10.807932

Transactions

1

Size

200 B

Version

2

Bits

0aced4a7

Nonce

1,802,434,319

Timestamp

12/30/2015, 12:45:43 AM

Confirmations

5,452,419

Merkle Root

d5e67e6dbbaa64b3c9a03eb4ef6fd323cc3e0ae68124af465990f80582eb1f18
Transactions (1)
Coinbased5e67e6dbbaa64…90f80582eb1f18
1 in β†’ 1 out8.5500 XPM110 B
AUfoV758…zYvAdedq
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.

1.421 Γ— 10⁹⁡(96-digit number)
14216406531121224703…80462266156027701120
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
1.421 Γ— 10⁹⁡(96-digit number)
14216406531121224703…80462266156027701119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.421 Γ— 10⁹⁡(96-digit number)
14216406531121224703…80462266156027701121
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
2.843 Γ— 10⁹⁡(96-digit number)
28432813062242449407…60924532312055402239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.843 Γ— 10⁹⁡(96-digit number)
28432813062242449407…60924532312055402241
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
5.686 Γ— 10⁹⁡(96-digit number)
56865626124484898814…21849064624110804479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.686 Γ— 10⁹⁡(96-digit number)
56865626124484898814…21849064624110804481
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
1.137 Γ— 10⁹⁢(97-digit number)
11373125224896979762…43698129248221608959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.137 Γ— 10⁹⁢(97-digit number)
11373125224896979762…43698129248221608961
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
2.274 Γ— 10⁹⁢(97-digit number)
22746250449793959525…87396258496443217919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.274 Γ— 10⁹⁢(97-digit number)
22746250449793959525…87396258496443217921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1390826

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 c3a504057fb2e0bb2088549d602befca8b3890ce1a3732be1b1c5f9a53760bb2

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 #1,390,826 on Chainz β†—
Circulating Supply:57,990,335 XPMΒ·at block #6,843,244 Β· updates every 60s
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