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Home/Chain Registry/Block #2,279,412

Block #2,279,412

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2017, 3:18:10 PM Β· Difficulty 10.9559 Β· 4,559,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8869475ecdefc2b2b5b99b161b22edf8f21fd2ff1d982b095bde6b31888cc4a2
View on Chainz β†—

Difficulty

10.955936

Transactions

1

Size

200 B

Version

2

Bits

0af4b836

Nonce

787,981,277

Timestamp

9/2/2017, 3:18:10 PM

Confirmations

4,559,466

Merkle Root

773258679620e3867ad8921d56edf10adab2394b26a939a8a762be33d3d0c63b
Transactions (1)
Coinbase773258679620e3…62be33d3d0c63b
1 in β†’ 1 out8.3200 XPM110 B
AeBEyaUP…QUuVw84J
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.

4.043 Γ— 10⁹⁡(96-digit number)
40431812748207347088…60956213322317045760
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
4.043 Γ— 10⁹⁡(96-digit number)
40431812748207347088…60956213322317045759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.043 Γ— 10⁹⁡(96-digit number)
40431812748207347088…60956213322317045761
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
8.086 Γ— 10⁹⁡(96-digit number)
80863625496414694176…21912426644634091519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.086 Γ— 10⁹⁡(96-digit number)
80863625496414694176…21912426644634091521
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
1.617 Γ— 10⁹⁢(97-digit number)
16172725099282938835…43824853289268183039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.617 Γ— 10⁹⁢(97-digit number)
16172725099282938835…43824853289268183041
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
3.234 Γ— 10⁹⁢(97-digit number)
32345450198565877670…87649706578536366079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.234 Γ— 10⁹⁢(97-digit number)
32345450198565877670…87649706578536366081
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
6.469 Γ— 10⁹⁢(97-digit number)
64690900397131755341…75299413157072732159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.469 Γ— 10⁹⁢(97-digit number)
64690900397131755341…75299413157072732161
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
1.293 Γ— 10⁹⁷(98-digit number)
12938180079426351068…50598826314145464319
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 2279412

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 8869475ecdefc2b2b5b99b161b22edf8f21fd2ff1d982b095bde6b31888cc4a2

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 #2,279,412 on Chainz β†—
Circulating Supply:57,955,292 XPMΒ·at block #6,838,877 Β· updates every 60s
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