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Home/Chain Registry/Block #471,895

Block #471,895

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/2/2014, 9:27:42 PM Β· Difficulty 10.4376 Β· 6,353,689 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
637502dadab1a883ad5fb7b0dab297aac2117a3d61e2abd9771d03ccd8e38b28
View on Chainz β†—

Height

#471,895

Difficulty

10.437630

Transactions

1

Size

200 B

Version

2

Bits

0a700880

Nonce

391,390

Timestamp

4/2/2014, 9:27:42 PM

Confirmations

6,353,689

Merkle Root

f8b4ebac580ff7de29fd86cc1c651d1b26940f22784339cf688e4fa234a22960
Transactions (1)
Coinbasef8b4ebac580ff7…8e4fa234a22960
1 in β†’ 1 out9.1600 XPM109 B
ARaPyHgj…nA9veLYH
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.

8.851 Γ— 10⁹⁷(98-digit number)
88512586271092757888…92353113774831028740
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
8.851 Γ— 10⁹⁷(98-digit number)
88512586271092757888…92353113774831028739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.770 Γ— 10⁹⁸(99-digit number)
17702517254218551577…84706227549662057479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.540 Γ— 10⁹⁸(99-digit number)
35405034508437103155…69412455099324114959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.081 Γ— 10⁹⁸(99-digit number)
70810069016874206311…38824910198648229919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁹(100-digit number)
14162013803374841262…77649820397296459839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.832 Γ— 10⁹⁹(100-digit number)
28324027606749682524…55299640794592919679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.664 Γ— 10⁹⁹(100-digit number)
56648055213499365048…10599281589185839359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.132 Γ— 10¹⁰⁰(101-digit number)
11329611042699873009…21198563178371678719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.265 Γ— 10¹⁰⁰(101-digit number)
22659222085399746019…42397126356743357439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.531 Γ— 10¹⁰⁰(101-digit number)
45318444170799492039…84794252713486714879
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 471895

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 637502dadab1a883ad5fb7b0dab297aac2117a3d61e2abd9771d03ccd8e38b28

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 #471,895 on Chainz β†—
Circulating Supply:57,848,771 XPMΒ·at block #6,825,583 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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