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Block #420,870

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/26/2014, 3:52:51 PM Β· Difficulty 10.3757 Β· 6,378,008 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
15f579a0e7a9537f65c984ac8c739f3abcea22d96ebaf0ac257bfb8ce24c9f1f
View on Chainz β†—

Height

#420,870

Difficulty

10.375688

Transactions

2

Size

393 B

Version

2

Bits

0a602d10

Nonce

226,492

Timestamp

2/26/2014, 3:52:51 PM

Confirmations

6,378,008

Merkle Root

3faa2d0f2812acffafce6f4df9599b9a5075632df0fbf9132cd1f1fa4adf0573
Transactions (2)
Coinbasec18a50fd259b13…cc85935fb92307
1 in β†’ 1 out9.2812 XPM110 B
AeKNrjNj…1NEq95Ta
64591e649689b1…f8cafe63820a5e
1 in β†’ 1 out2.9900 XPM193 B
AZnYPcsN…ygU2ETg2
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.

6.656 Γ— 10⁹⁡(96-digit number)
66568775720918746781…30262814094349216000
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
6.656 Γ— 10⁹⁡(96-digit number)
66568775720918746781…30262814094349216001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.331 Γ— 10⁹⁢(97-digit number)
13313755144183749356…60525628188698432001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.662 Γ— 10⁹⁢(97-digit number)
26627510288367498712…21051256377396864001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.325 Γ— 10⁹⁢(97-digit number)
53255020576734997425…42102512754793728001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.065 Γ— 10⁹⁷(98-digit number)
10651004115346999485…84205025509587456001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.130 Γ— 10⁹⁷(98-digit number)
21302008230693998970…68410051019174912001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.260 Γ— 10⁹⁷(98-digit number)
42604016461387997940…36820102038349824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.520 Γ— 10⁹⁷(98-digit number)
85208032922775995880…73640204076699648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.704 Γ— 10⁹⁸(99-digit number)
17041606584555199176…47280408153399296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.408 Γ— 10⁹⁸(99-digit number)
34083213169110398352…94560816306798592001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 420870

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 15f579a0e7a9537f65c984ac8c739f3abcea22d96ebaf0ac257bfb8ce24c9f1f

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 #420,870 on Chainz β†—
Circulating Supply:57,635,061 XPMΒ·at block #6,798,877 Β· updates every 60s
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