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Home/Chain Registry/Block #2,932,967

Block #2,932,967

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/21/2018, 12:46:31 PM Β· Difficulty 11.3975 Β· 3,899,648 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
416244c3cefd27d68204674813d4d1a7c0a7cd21ae3ec198a420b8a8f2212baa
View on Chainz β†—

Difficulty

11.397476

Transactions

1

Size

201 B

Version

2

Bits

0b65c105

Nonce

1,714,922,471

Timestamp

11/21/2018, 12:46:31 PM

Confirmations

3,899,648

Merkle Root

16bee00dd23c66510e0d83d61f1aa576f58a5c7bdd98b2590708a4d32da0bbf4
Transactions (1)
Coinbase16bee00dd23c66…08a4d32da0bbf4
1 in β†’ 1 out7.6900 XPM110 B
AbXwmGxD…4XXYP765
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.

3.385 Γ— 10⁹⁷(98-digit number)
33854491803136018365…16901256405354455040
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
3.385 Γ— 10⁹⁷(98-digit number)
33854491803136018365…16901256405354455041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.770 Γ— 10⁹⁷(98-digit number)
67708983606272036731…33802512810708910081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.354 Γ— 10⁹⁸(99-digit number)
13541796721254407346…67605025621417820161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.708 Γ— 10⁹⁸(99-digit number)
27083593442508814692…35210051242835640321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.416 Γ— 10⁹⁸(99-digit number)
54167186885017629385…70420102485671280641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.083 Γ— 10⁹⁹(100-digit number)
10833437377003525877…40840204971342561281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.166 Γ— 10⁹⁹(100-digit number)
21666874754007051754…81680409942685122561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.333 Γ— 10⁹⁹(100-digit number)
43333749508014103508…63360819885370245121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.666 Γ— 10⁹⁹(100-digit number)
86667499016028207016…26721639770740490241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.733 Γ— 10¹⁰⁰(101-digit number)
17333499803205641403…53443279541480980481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.466 Γ— 10¹⁰⁰(101-digit number)
34666999606411282806…06886559082961960961
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 2932967

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 416244c3cefd27d68204674813d4d1a7c0a7cd21ae3ec198a420b8a8f2212baa

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 #2,932,967 on Chainz β†—
Circulating Supply:57,905,066 XPMΒ·at block #6,832,614 Β· updates every 60s
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