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Home/Chain Registry/Block #2,079,075

Block #2,079,075

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/20/2017, 7:17:55 AM Β· Difficulty 10.8577 Β· 4,754,613 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9ef72e04624533e3d07e4007b7e854435a265ccf57905f1b470f4b61544ffc0a
View on Chainz β†—

Difficulty

10.857723

Transactions

1

Size

199 B

Version

2

Bits

0adb93c1

Nonce

116,982,467

Timestamp

4/20/2017, 7:17:55 AM

Confirmations

4,754,613

Merkle Root

7449458ed8c81690afe134840dad47cc5f809f5a5777544deab861203e846f5d
Transactions (1)
Coinbase7449458ed8c816…b861203e846f5d
1 in β†’ 1 out8.4700 XPM109 B
AbaMVKKp…9PHBGPVP
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.

7.190 Γ— 10⁹⁡(96-digit number)
71907727332075593381…56436269916529694400
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
7.190 Γ— 10⁹⁡(96-digit number)
71907727332075593381…56436269916529694399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.190 Γ— 10⁹⁡(96-digit number)
71907727332075593381…56436269916529694401
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
1.438 Γ— 10⁹⁢(97-digit number)
14381545466415118676…12872539833059388799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.438 Γ— 10⁹⁢(97-digit number)
14381545466415118676…12872539833059388801
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
2.876 Γ— 10⁹⁢(97-digit number)
28763090932830237352…25745079666118777599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.876 Γ— 10⁹⁢(97-digit number)
28763090932830237352…25745079666118777601
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
5.752 Γ— 10⁹⁢(97-digit number)
57526181865660474704…51490159332237555199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.752 Γ— 10⁹⁢(97-digit number)
57526181865660474704…51490159332237555201
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
1.150 Γ— 10⁹⁷(98-digit number)
11505236373132094940…02980318664475110399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.150 Γ— 10⁹⁷(98-digit number)
11505236373132094940…02980318664475110401
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 2079075

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 9ef72e04624533e3d07e4007b7e854435a265ccf57905f1b470f4b61544ffc0a

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 #2,079,075 on Chainz β†—
Circulating Supply:57,913,725 XPMΒ·at block #6,833,687 Β· updates every 60s
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