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Block #462,168

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/27/2014, 6:50:16 AM Β· Difficulty 10.4085 Β· 6,352,180 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f48be996b9c37298b87f89bece927c58ff5d537f2ea3968934b5a8a75b31af86
View on Chainz β†—

Height

#462,168

Difficulty

10.408544

Transactions

1

Size

202 B

Version

2

Bits

0a689650

Nonce

212,312

Timestamp

3/27/2014, 6:50:16 AM

Confirmations

6,352,180

Merkle Root

6245f945d7cf41c6fac33c9ef749ee17b3c7a3e4b68394b3f1a10e6df9c97b46
Transactions (1)
Coinbase6245f945d7cf41…a10e6df9c97b46
1 in β†’ 1 out9.2200 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.

1.484 Γ— 10⁹⁹(100-digit number)
14846218500187990535…85661999587889377280
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
1.484 Γ— 10⁹⁹(100-digit number)
14846218500187990535…85661999587889377279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.969 Γ— 10⁹⁹(100-digit number)
29692437000375981071…71323999175778754559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.938 Γ— 10⁹⁹(100-digit number)
59384874000751962142…42647998351557509119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.187 Γ— 10¹⁰⁰(101-digit number)
11876974800150392428…85295996703115018239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.375 Γ— 10¹⁰⁰(101-digit number)
23753949600300784857…70591993406230036479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.750 Γ— 10¹⁰⁰(101-digit number)
47507899200601569714…41183986812460072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.501 Γ— 10¹⁰⁰(101-digit number)
95015798401203139428…82367973624920145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.900 Γ— 10¹⁰¹(102-digit number)
19003159680240627885…64735947249840291839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.800 Γ— 10¹⁰¹(102-digit number)
38006319360481255771…29471894499680583679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.601 Γ— 10¹⁰¹(102-digit number)
76012638720962511543…58943788999361167359
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 462168

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 f48be996b9c37298b87f89bece927c58ff5d537f2ea3968934b5a8a75b31af86

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 #462,168 on Chainz β†—
Circulating Supply:57,758,848 XPMΒ·at block #6,814,347 Β· updates every 60s
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