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Home/Chain Registry/Block #2,051,422

Block #2,051,422

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2017, 12:33:52 PM Β· Difficulty 10.7137 Β· 4,790,924 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a8eccd0b6c8892a343d284b5645c93d1d3e7e568c02e96005143d98390728d70
View on Chainz β†—

Difficulty

10.713670

Transactions

1

Size

199 B

Version

2

Bits

0ab6b318

Nonce

1,549,905,023

Timestamp

4/3/2017, 12:33:52 PM

Confirmations

4,790,924

Merkle Root

35ae242efb4a2993a3f98231c4dee019e520ed937cd393dcc43fee8f7efbf477
Transactions (1)
Coinbase35ae242efb4a29…3fee8f7efbf477
1 in β†’ 1 out8.7000 XPM109 B
ALCvwQBL…7pM6evCp
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.

1.154 Γ— 10⁹⁡(96-digit number)
11549069784789320684…11905986202330946160
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
1.154 Γ— 10⁹⁡(96-digit number)
11549069784789320684…11905986202330946159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.154 Γ— 10⁹⁡(96-digit number)
11549069784789320684…11905986202330946161
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
2.309 Γ— 10⁹⁡(96-digit number)
23098139569578641369…23811972404661892319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.309 Γ— 10⁹⁡(96-digit number)
23098139569578641369…23811972404661892321
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
4.619 Γ— 10⁹⁡(96-digit number)
46196279139157282739…47623944809323784639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.619 Γ— 10⁹⁡(96-digit number)
46196279139157282739…47623944809323784641
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
9.239 Γ— 10⁹⁡(96-digit number)
92392558278314565479…95247889618647569279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.239 Γ— 10⁹⁡(96-digit number)
92392558278314565479…95247889618647569281
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
1.847 Γ— 10⁹⁢(97-digit number)
18478511655662913095…90495779237295138559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.847 Γ— 10⁹⁢(97-digit number)
18478511655662913095…90495779237295138561
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 2051422

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 a8eccd0b6c8892a343d284b5645c93d1d3e7e568c02e96005143d98390728d70

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 #2,051,422 on Chainz β†—
Circulating Supply:57,983,173 XPMΒ·at block #6,842,345 Β· updates every 60s
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