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Block #64,021

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 5:12:50 AM Β· Difficulty 8.9806 Β· 6,730,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d87061c243f8420d50b9059a27c8cb593f5d4b6644e2d2b82623ac7edacdc350
View on Chainz β†—

Height

#64,021

Difficulty

8.980619

Transactions

1

Size

197 B

Version

2

Bits

08fb09d3

Nonce

56

Timestamp

7/19/2013, 5:12:50 AM

Confirmations

6,730,593

Merkle Root

7694651690837c798452eb8f6dff4d4c683d66a5e972521042555343d373b028
Transactions (1)
Coinbase7694651690837c…555343d373b028
1 in β†’ 1 out12.3800 XPM110 B
ALpmZjzw…SUr8YMD5
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.

3.689 Γ— 10⁸⁸(89-digit number)
36890583311066241235…81141800371798616750
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
3.689 Γ— 10⁸⁸(89-digit number)
36890583311066241235…81141800371798616751
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.378 Γ— 10⁸⁸(89-digit number)
73781166622132482470…62283600743597233501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.475 Γ— 10⁸⁹(90-digit number)
14756233324426496494…24567201487194467001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.951 Γ— 10⁸⁹(90-digit number)
29512466648852992988…49134402974388934001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.902 Γ— 10⁸⁹(90-digit number)
59024933297705985976…98268805948777868001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.180 Γ— 10⁹⁰(91-digit number)
11804986659541197195…96537611897555736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.360 Γ— 10⁹⁰(91-digit number)
23609973319082394390…93075223795111472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.721 Γ— 10⁹⁰(91-digit number)
47219946638164788780…86150447590222944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.443 Γ— 10⁹⁰(91-digit number)
94439893276329577561…72300895180445888001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 64021

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 d87061c243f8420d50b9059a27c8cb593f5d4b6644e2d2b82623ac7edacdc350

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 #64,021 on Chainz β†—
Circulating Supply:57,600,955 XPMΒ·at block #6,794,613 Β· updates every 60s
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