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Block #486,292

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/11/2014, 12:40:51 PM Β· Difficulty 10.6231 Β· 6,325,502 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4ccd330e45cf8a406efb26f984f2549e5aaaa11b31575ac24a89bcb165a26bbe
View on Chainz β†—

Height

#486,292

Difficulty

10.623102

Transactions

1

Size

208 B

Version

2

Bits

0a9f839a

Nonce

17,599,082

Timestamp

4/11/2014, 12:40:51 PM

Confirmations

6,325,502

Merkle Root

3a151bd5bdf1339da7d6f119eae254dcfd44b07bfe2b56bc5a43a2186d9616a7
Transactions (1)
Coinbase3a151bd5bdf133…43a2186d9616a7
1 in β†’ 1 out8.8500 XPM116 B
AbwWkWZt…kawDhufa
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.

4.732 Γ— 10⁹⁸(99-digit number)
47327224998313610096…57456978078480391360
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
4.732 Γ— 10⁹⁸(99-digit number)
47327224998313610096…57456978078480391359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.465 Γ— 10⁹⁸(99-digit number)
94654449996627220193…14913956156960782719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.893 Γ— 10⁹⁹(100-digit number)
18930889999325444038…29827912313921565439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.786 Γ— 10⁹⁹(100-digit number)
37861779998650888077…59655824627843130879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.572 Γ— 10⁹⁹(100-digit number)
75723559997301776154…19311649255686261759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.514 Γ— 10¹⁰⁰(101-digit number)
15144711999460355230…38623298511372523519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.028 Γ— 10¹⁰⁰(101-digit number)
30289423998920710461…77246597022745047039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.057 Γ— 10¹⁰⁰(101-digit number)
60578847997841420923…54493194045490094079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.211 Γ— 10¹⁰¹(102-digit number)
12115769599568284184…08986388090980188159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.423 Γ— 10¹⁰¹(102-digit number)
24231539199136568369…17972776181960376319
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 486292

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 4ccd330e45cf8a406efb26f984f2549e5aaaa11b31575ac24a89bcb165a26bbe

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 #486,292 on Chainz β†—
Circulating Supply:57,738,464 XPMΒ·at block #6,811,793 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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