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Block #492,291

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/15/2014, 12:52:45 AM Β· Difficulty 10.6887 Β· 6,323,779 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
292ff6c48c11b4c4d3f4e2a79b856a2f48dcdc26e30a4ec6bfb130534bbf4676
View on Chainz β†—

Height

#492,291

Difficulty

10.688678

Transactions

1

Size

199 B

Version

2

Bits

0ab04d32

Nonce

6,837,574

Timestamp

4/15/2014, 12:52:45 AM

Confirmations

6,323,779

Merkle Root

0e34f3e40adac26bfc46a5bd14bcb802dc44be8e19ad2d4d45536e3febc0f248
Transactions (1)
Coinbase0e34f3e40adac2…536e3febc0f248
1 in β†’ 1 out8.7400 XPM109 B
AVNDoLaA…7Y4W1xty
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.

1.872 Γ— 10⁹⁴(95-digit number)
18729878701803833931…76804480133485664640
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
1.872 Γ— 10⁹⁴(95-digit number)
18729878701803833931…76804480133485664639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.745 Γ— 10⁹⁴(95-digit number)
37459757403607667862…53608960266971329279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.491 Γ— 10⁹⁴(95-digit number)
74919514807215335725…07217920533942658559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.498 Γ— 10⁹⁡(96-digit number)
14983902961443067145…14435841067885317119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.996 Γ— 10⁹⁡(96-digit number)
29967805922886134290…28871682135770634239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.993 Γ— 10⁹⁡(96-digit number)
59935611845772268580…57743364271541268479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.198 Γ— 10⁹⁢(97-digit number)
11987122369154453716…15486728543082536959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.397 Γ— 10⁹⁢(97-digit number)
23974244738308907432…30973457086165073919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.794 Γ— 10⁹⁢(97-digit number)
47948489476617814864…61946914172330147839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.589 Γ— 10⁹⁢(97-digit number)
95896978953235629728…23893828344660295679
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 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
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 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 492291

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 292ff6c48c11b4c4d3f4e2a79b856a2f48dcdc26e30a4ec6bfb130534bbf4676

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 #492,291 on Chainz β†—
Circulating Supply:57,772,677 XPMΒ·at block #6,816,069 Β· updates every 60s
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