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Block #64,023

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 5:13:16 AM Β· Difficulty 8.9806 Β· 6,762,390 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
066c1812de383e386b181f649195bcfc9c6282d945aced211110de346541eb0c
View on Chainz β†—

Height

#64,023

Difficulty

8.980625

Transactions

1

Size

201 B

Version

2

Bits

08fb0a37

Nonce

507

Timestamp

7/19/2013, 5:13:16 AM

Confirmations

6,762,390

Merkle Root

df6e223367315a4cf93a1140b77ee905638bd4c89af97cf3e51103e6f88a9be5
Transactions (1)
Coinbasedf6e223367315a…1103e6f88a9be5
1 in β†’ 1 out12.3800 XPM110 B
AZakk5h5…giTZcejN
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.

1.882 Γ— 10⁹⁢(97-digit number)
18823558628413422564…10927170040788365460
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
1.882 Γ— 10⁹⁢(97-digit number)
18823558628413422564…10927170040788365461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.764 Γ— 10⁹⁢(97-digit number)
37647117256826845129…21854340081576730921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.529 Γ— 10⁹⁢(97-digit number)
75294234513653690259…43708680163153461841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.505 Γ— 10⁹⁷(98-digit number)
15058846902730738051…87417360326306923681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.011 Γ— 10⁹⁷(98-digit number)
30117693805461476103…74834720652613847361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.023 Γ— 10⁹⁷(98-digit number)
60235387610922952207…49669441305227694721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.204 Γ— 10⁹⁸(99-digit number)
12047077522184590441…99338882610455389441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.409 Γ— 10⁹⁸(99-digit number)
24094155044369180882…98677765220910778881
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 64023

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 066c1812de383e386b181f649195bcfc9c6282d945aced211110de346541eb0c

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 #64,023 on Chainz β†—
Circulating Supply:57,855,437 XPMΒ·at block #6,826,412 Β· updates every 60s
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