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Block #174,373

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2013, 3:09:37 PM Β· Difficulty 9.8611 Β· 6,637,846 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2720cf5f9da3e21a47b39ab4c1bd134fc8ab9e2dfbc3f2e524479ed618bf212f
View on Chainz β†—

Height

#174,373

Difficulty

9.861080

Transactions

1

Size

204 B

Version

2

Bits

09dc6fbd

Nonce

197,046

Timestamp

9/21/2013, 3:09:37 PM

Confirmations

6,637,846

Merkle Root

fee2866e95317e9a7cfa30823783ecdfc0926ff6d8684f8b4923f1590feceb68
Transactions (1)
Coinbasefee2866e95317e…23f1590feceb68
1 in β†’ 1 out10.2700 XPM112 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.

4.982 Γ— 10⁹⁹(100-digit number)
49825449173469165987…78676264940541690280
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
4.982 Γ— 10⁹⁹(100-digit number)
49825449173469165987…78676264940541690281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.965 Γ— 10⁹⁹(100-digit number)
99650898346938331974…57352529881083380561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.993 Γ— 10¹⁰⁰(101-digit number)
19930179669387666394…14705059762166761121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.986 Γ— 10¹⁰⁰(101-digit number)
39860359338775332789…29410119524333522241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.972 Γ— 10¹⁰⁰(101-digit number)
79720718677550665579…58820239048667044481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.594 Γ— 10¹⁰¹(102-digit number)
15944143735510133115…17640478097334088961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.188 Γ— 10¹⁰¹(102-digit number)
31888287471020266231…35280956194668177921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.377 Γ— 10¹⁰¹(102-digit number)
63776574942040532463…70561912389336355841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.275 Γ— 10¹⁰²(103-digit number)
12755314988408106492…41123824778672711681
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 174373

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 2720cf5f9da3e21a47b39ab4c1bd134fc8ab9e2dfbc3f2e524479ed618bf212f

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 #174,373 on Chainz β†—
Circulating Supply:57,741,766 XPMΒ·at block #6,812,218 Β· updates every 60s
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