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Block #31,072

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 9:53:56 PM Β· Difficulty 7.9880 Β· 6,782,832 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f724408070bd4c08c4db7f77ac80c8ab7daaf7d958a850e437444abba6f8cfee
View on Chainz β†—

Height

#31,072

Difficulty

7.988049

Transactions

1

Size

203 B

Version

2

Bits

07fcf0c1

Nonce

932

Timestamp

7/13/2013, 9:53:56 PM

Confirmations

6,782,832

Merkle Root

1aa0d7f75095a3bbf68bb26520f3935d001720216799ef70760bf138a1b32b4e
Transactions (1)
Coinbase1aa0d7f75095a3…0bf138a1b32b4e
1 in β†’ 1 out15.6500 XPM109 B
AV6P7enU…VLHeixvR
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.

1.802 Γ— 10¹⁰⁡(106-digit number)
18028217841319747731…54715074001064424080
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
1.802 Γ— 10¹⁰⁡(106-digit number)
18028217841319747731…54715074001064424081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.605 Γ— 10¹⁰⁡(106-digit number)
36056435682639495462…09430148002128848161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.211 Γ— 10¹⁰⁡(106-digit number)
72112871365278990924…18860296004257696321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.442 Γ— 10¹⁰⁢(107-digit number)
14422574273055798184…37720592008515392641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.884 Γ— 10¹⁰⁢(107-digit number)
28845148546111596369…75441184017030785281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.769 Γ— 10¹⁰⁢(107-digit number)
57690297092223192739…50882368034061570561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.153 Γ— 10¹⁰⁷(108-digit number)
11538059418444638547…01764736068123141121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.307 Γ— 10¹⁰⁷(108-digit number)
23076118836889277095…03529472136246282241
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 31072

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 f724408070bd4c08c4db7f77ac80c8ab7daaf7d958a850e437444abba6f8cfee

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 #31,072 on Chainz β†—
Circulating Supply:57,755,311 XPMΒ·at block #6,813,903 Β· updates every 60s
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