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Block #421,792

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/27/2014, 7:18:46 AM Β· Difficulty 10.3753 Β· 6,405,352 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cf1a8bc50f3d8c17b6b554306bfba6aa10055e5ad367513fffc09c9c6b4973f
View on Chainz β†—

Height

#421,792

Difficulty

10.375254

Transactions

1

Size

202 B

Version

2

Bits

0a6010ac

Nonce

83,360

Timestamp

2/27/2014, 7:18:46 AM

Confirmations

6,405,352

Merkle Root

692649ebfb24fc36601dc9002ee7303826b7aaebaf4e8ebad863db6f6be1d8a9
Transactions (1)
Coinbase692649ebfb24fc…63db6f6be1d8a9
1 in β†’ 1 out9.2800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

2.553 Γ— 10⁹⁸(99-digit number)
25539168455302935938…89594437217863092720
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
2.553 Γ— 10⁹⁸(99-digit number)
25539168455302935938…89594437217863092719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.107 Γ— 10⁹⁸(99-digit number)
51078336910605871877…79188874435726185439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.021 Γ— 10⁹⁹(100-digit number)
10215667382121174375…58377748871452370879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.043 Γ— 10⁹⁹(100-digit number)
20431334764242348750…16755497742904741759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.086 Γ— 10⁹⁹(100-digit number)
40862669528484697501…33510995485809483519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.172 Γ— 10⁹⁹(100-digit number)
81725339056969395003…67021990971618967039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.634 Γ— 10¹⁰⁰(101-digit number)
16345067811393879000…34043981943237934079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.269 Γ— 10¹⁰⁰(101-digit number)
32690135622787758001…68087963886475868159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.538 Γ— 10¹⁰⁰(101-digit number)
65380271245575516002…36175927772951736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.307 Γ— 10¹⁰¹(102-digit number)
13076054249115103200…72351855545903472639
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 421792

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 4cf1a8bc50f3d8c17b6b554306bfba6aa10055e5ad367513fffc09c9c6b4973f

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 #421,792 on Chainz β†—
Circulating Supply:57,861,334 XPMΒ·at block #6,827,143 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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