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Block #225,073

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/24/2013, 5:53:19 AM Β· Difficulty 9.9366 Β· 6,617,809 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a38e493a9fdfb3773ff92b40f2ef39db422978f0a4192857b181c07e923ec5ed
View on Chainz β†—

Height

#225,073

Difficulty

9.936590

Transactions

1

Size

210 B

Version

2

Bits

09efc456

Nonce

167,772,692

Timestamp

10/24/2013, 5:53:19 AM

Confirmations

6,617,809

Merkle Root

dcfb2ab064a1c96c1c9846bf7560bac6fcb012f4052eb39d1cdb3fd4e7879dd1
Transactions (1)
Coinbasedcfb2ab064a1c9…db3fd4e7879dd1
1 in β†’ 1 out10.1100 XPM116 B
AcLBm5Z9…S683d7c3
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.

7.398 Γ— 10¹⁰⁴(105-digit number)
73988813876867572812…90743997970143856480
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
7.398 Γ— 10¹⁰⁴(105-digit number)
73988813876867572812…90743997970143856481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.479 Γ— 10¹⁰⁡(106-digit number)
14797762775373514562…81487995940287712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.959 Γ— 10¹⁰⁡(106-digit number)
29595525550747029125…62975991880575425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.919 Γ— 10¹⁰⁡(106-digit number)
59191051101494058250…25951983761150851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.183 Γ— 10¹⁰⁢(107-digit number)
11838210220298811650…51903967522301703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.367 Γ— 10¹⁰⁢(107-digit number)
23676420440597623300…03807935044603407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.735 Γ— 10¹⁰⁢(107-digit number)
47352840881195246600…07615870089206814721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.470 Γ— 10¹⁰⁢(107-digit number)
94705681762390493200…15231740178413629441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.894 Γ— 10¹⁰⁷(108-digit number)
18941136352478098640…30463480356827258881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.788 Γ— 10¹⁰⁷(108-digit number)
37882272704956197280…60926960713654517761
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 225073

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 a38e493a9fdfb3773ff92b40f2ef39db422978f0a4192857b181c07e923ec5ed

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 #225,073 on Chainz β†—
Circulating Supply:57,987,401 XPMΒ·at block #6,842,881 Β· updates every 60s
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