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Block #846,172

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/9/2014, 10:12:54 AM Β· Difficulty 10.9723 Β· 5,994,941 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc930886535c1e0e57437ae02fd1ad3f44589d02d2801f16f92cf72d1e1128ec
View on Chainz β†—

Height

#846,172

Difficulty

10.972294

Transactions

1

Size

200 B

Version

2

Bits

0af8e849

Nonce

1,575,002,668

Timestamp

12/9/2014, 10:12:54 AM

Confirmations

5,994,941

Merkle Root

9eeda5178bfd57979e9b30de999dfed3e14846a542d00a57633aaf9acf2dc455
Transactions (1)
Coinbase9eeda5178bfd57…3aaf9acf2dc455
1 in β†’ 1 out8.2900 XPM110 B
AQ67NGfo…GNwMVJ9s
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.

1.599 Γ— 10⁹⁴(95-digit number)
15992058351386155241…66427413629683450880
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.599 Γ— 10⁹⁴(95-digit number)
15992058351386155241…66427413629683450879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.198 Γ— 10⁹⁴(95-digit number)
31984116702772310482…32854827259366901759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.396 Γ— 10⁹⁴(95-digit number)
63968233405544620965…65709654518733803519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.279 Γ— 10⁹⁡(96-digit number)
12793646681108924193…31419309037467607039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.558 Γ— 10⁹⁡(96-digit number)
25587293362217848386…62838618074935214079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.117 Γ— 10⁹⁡(96-digit number)
51174586724435696772…25677236149870428159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.023 Γ— 10⁹⁢(97-digit number)
10234917344887139354…51354472299740856319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.046 Γ— 10⁹⁢(97-digit number)
20469834689774278708…02708944599481712639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.093 Γ— 10⁹⁢(97-digit number)
40939669379548557417…05417889198963425279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.187 Γ— 10⁹⁢(97-digit number)
81879338759097114835…10835778397926850559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.637 Γ— 10⁹⁷(98-digit number)
16375867751819422967…21671556795853701119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 846172

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 bc930886535c1e0e57437ae02fd1ad3f44589d02d2801f16f92cf72d1e1128ec

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 #846,172 on Chainz β†—
Circulating Supply:57,973,271 XPMΒ·at block #6,841,112 Β· updates every 60s
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