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Home/Chain Registry/Block #2,831,865

Block #2,831,865

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/9/2018, 2:57:02 PM Β· Difficulty 11.7186 Β· 4,012,596 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fb60521aea7a5f2e5a5754aa39781c69a7e411ac9eff20fc51e6ecdd409cc9ad
View on Chainz β†—

Difficulty

11.718578

Transactions

1

Size

201 B

Version

2

Bits

0bb7f4c2

Nonce

1,156,287,151

Timestamp

9/9/2018, 2:57:02 PM

Confirmations

4,012,596

Merkle Root

c067d9c16c8ec7d70072c708b4da9cbd20f8e6bcf5dd61eba820c958b0bdda1f
Transactions (1)
Coinbasec067d9c16c8ec7…20c958b0bdda1f
1 in β†’ 1 out7.2700 XPM110 B
AProFAhf…LP9d8zTo
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.

6.183 Γ— 10⁹⁢(97-digit number)
61833545317014344534…38308714453627852800
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
6.183 Γ— 10⁹⁢(97-digit number)
61833545317014344534…38308714453627852801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.236 Γ— 10⁹⁷(98-digit number)
12366709063402868906…76617428907255705601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.473 Γ— 10⁹⁷(98-digit number)
24733418126805737813…53234857814511411201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.946 Γ— 10⁹⁷(98-digit number)
49466836253611475627…06469715629022822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.893 Γ— 10⁹⁷(98-digit number)
98933672507222951255…12939431258045644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.978 Γ— 10⁹⁸(99-digit number)
19786734501444590251…25878862516091289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.957 Γ— 10⁹⁸(99-digit number)
39573469002889180502…51757725032182579201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.914 Γ— 10⁹⁸(99-digit number)
79146938005778361004…03515450064365158401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.582 Γ— 10⁹⁹(100-digit number)
15829387601155672200…07030900128730316801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.165 Γ— 10⁹⁹(100-digit number)
31658775202311344401…14061800257460633601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.331 Γ— 10⁹⁹(100-digit number)
63317550404622688803…28123600514921267201
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 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
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 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 2831865

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 fb60521aea7a5f2e5a5754aa39781c69a7e411ac9eff20fc51e6ecdd409cc9ad

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 #2,831,865 on Chainz β†—
Circulating Supply:58,000,083 XPMΒ·at block #6,844,460 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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