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Home/Chain Registry/Block #2,091,337

Block #2,091,337

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2017, 10:38:36 AM Β· Difficulty 10.8726 Β· 4,739,918 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
10542b0f4bbbd9af5ac1ec3e13326b1ffe67322025f7d67873954ec8e25a4920
View on Chainz β†—

Difficulty

10.872595

Transactions

1

Size

200 B

Version

2

Bits

0adf6265

Nonce

663,560,231

Timestamp

4/28/2017, 10:38:36 AM

Confirmations

4,739,918

Merkle Root

3c50e17d9dd55a8eeb6699739ff185a32525349bec4f4cef7b17f663ad90adc9
Transactions (1)
Coinbase3c50e17d9dd55a…17f663ad90adc9
1 in β†’ 1 out8.4500 XPM109 B
AZQxadX1…Msj7wNu6
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.

1.087 Γ— 10⁹⁢(97-digit number)
10878943136335781371…07242299984924487680
Discovered Prime Numbers
p_k = 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.

1
origin + 1
1.087 Γ— 10⁹⁢(97-digit number)
10878943136335781371…07242299984924487681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.175 Γ— 10⁹⁢(97-digit number)
21757886272671562743…14484599969848975361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.351 Γ— 10⁹⁢(97-digit number)
43515772545343125487…28969199939697950721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.703 Γ— 10⁹⁢(97-digit number)
87031545090686250974…57938399879395901441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.740 Γ— 10⁹⁷(98-digit number)
17406309018137250194…15876799758791802881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.481 Γ— 10⁹⁷(98-digit number)
34812618036274500389…31753599517583605761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.962 Γ— 10⁹⁷(98-digit number)
69625236072549000779…63507199035167211521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.392 Γ— 10⁹⁸(99-digit number)
13925047214509800155…27014398070334423041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.785 Γ— 10⁹⁸(99-digit number)
27850094429019600311…54028796140668846081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.570 Γ— 10⁹⁸(99-digit number)
55700188858039200623…08057592281337692161
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 2091337

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 10542b0f4bbbd9af5ac1ec3e13326b1ffe67322025f7d67873954ec8e25a4920

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 #2,091,337 on Chainz β†—
Circulating Supply:57,894,190 XPMΒ·at block #6,831,254 Β· updates every 60s
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