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Home/Chain Registry/Block #2,094,825

Block #2,094,825

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2017, 9:17:21 PM Β· Difficulty 10.8720 Β· 4,749,084 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d6f228d7af3d3d7b355849a858d0de1cf1190d73b99e92644d82ea6f7ace745
View on Chainz β†—

Difficulty

10.871958

Transactions

1

Size

199 B

Version

2

Bits

0adf38a5

Nonce

1,046,875,319

Timestamp

4/30/2017, 9:17:21 PM

Confirmations

4,749,084

Merkle Root

e08076fd89e879924b3a81569a781ac7f2d70487858557e3be4f7705497f8934
Transactions (1)
Coinbasee08076fd89e879…4f7705497f8934
1 in β†’ 1 out8.4500 XPM109 B
AUDntJTa…WGHgNx3c
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.

2.147 Γ— 10⁹⁴(95-digit number)
21476254071280851903…86658985952016904320
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
2.147 Γ— 10⁹⁴(95-digit number)
21476254071280851903…86658985952016904321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.295 Γ— 10⁹⁴(95-digit number)
42952508142561703807…73317971904033808641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.590 Γ— 10⁹⁴(95-digit number)
85905016285123407615…46635943808067617281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.718 Γ— 10⁹⁡(96-digit number)
17181003257024681523…93271887616135234561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.436 Γ— 10⁹⁡(96-digit number)
34362006514049363046…86543775232270469121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.872 Γ— 10⁹⁡(96-digit number)
68724013028098726092…73087550464540938241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.374 Γ— 10⁹⁢(97-digit number)
13744802605619745218…46175100929081876481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.748 Γ— 10⁹⁢(97-digit number)
27489605211239490437…92350201858163752961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.497 Γ— 10⁹⁢(97-digit number)
54979210422478980874…84700403716327505921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.099 Γ— 10⁹⁷(98-digit number)
10995842084495796174…69400807432655011841
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 2094825

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 0d6f228d7af3d3d7b355849a858d0de1cf1190d73b99e92644d82ea6f7ace745

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 #2,094,825 on Chainz β†—
Circulating Supply:57,995,642 XPMΒ·at block #6,843,908 Β· updates every 60s
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