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Block #832,279

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/28/2014, 7:02:48 PM Β· Difficulty 10.9787 Β· 6,010,510 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d00ebef8445fa10a83b0b0bc31a33da0f4e6cd507ff48b6ae321929baeb7ac3
View on Chainz β†—

Height

#832,279

Difficulty

10.978729

Transactions

1

Size

207 B

Version

2

Bits

0afa8dfd

Nonce

1,904,354,981

Timestamp

11/28/2014, 7:02:48 PM

Confirmations

6,010,510

Merkle Root

753b0803236a2f444d7fd4a4a7fd53d75a30d738c6765966a2d062a169418c4d
Transactions (1)
Coinbase753b0803236a2f…d062a169418c4d
1 in β†’ 1 out8.2800 XPM116 B
ANSXnLY2…Sd25TjkD
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.

9.546 Γ— 10⁹⁢(97-digit number)
95464782428553953340…40144961655665873600
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
9.546 Γ— 10⁹⁢(97-digit number)
95464782428553953340…40144961655665873601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.909 Γ— 10⁹⁷(98-digit number)
19092956485710790668…80289923311331747201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.818 Γ— 10⁹⁷(98-digit number)
38185912971421581336…60579846622663494401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.637 Γ— 10⁹⁷(98-digit number)
76371825942843162672…21159693245326988801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.527 Γ— 10⁹⁸(99-digit number)
15274365188568632534…42319386490653977601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.054 Γ— 10⁹⁸(99-digit number)
30548730377137265068…84638772981307955201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.109 Γ— 10⁹⁸(99-digit number)
61097460754274530137…69277545962615910401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.221 Γ— 10⁹⁹(100-digit number)
12219492150854906027…38555091925231820801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.443 Γ— 10⁹⁹(100-digit number)
24438984301709812055…77110183850463641601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.887 Γ— 10⁹⁹(100-digit number)
48877968603419624110…54220367700927283201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.775 Γ— 10⁹⁹(100-digit number)
97755937206839248220…08440735401854566401
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 832279

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 0d00ebef8445fa10a83b0b0bc31a33da0f4e6cd507ff48b6ae321929baeb7ac3

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 #832,279 on Chainz β†—
Circulating Supply:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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