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Block #174,027

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/21/2013, 9:46:07 AM Β· Difficulty 9.8605 Β· 6,653,202 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5e355da737ca9982008f80454fa3479ff5d087b2708f2862b13f15c55724e2e8
View on Chainz β†—

Height

#174,027

Difficulty

9.860452

Transactions

1

Size

198 B

Version

2

Bits

09dc4696

Nonce

28,310

Timestamp

9/21/2013, 9:46:07 AM

Confirmations

6,653,202

Merkle Root

2ba4ec5f128f92b1267c7d8ffb1fbef389b7ee5ad6d042f07ffd52bf741dbc54
Transactions (1)
Coinbase2ba4ec5f128f92…fd52bf741dbc54
1 in β†’ 1 out10.2700 XPM109 B
Ae6PYBDN…jSQhB18y
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.

7.772 Γ— 10⁹²(93-digit number)
77720170555152909354…20213176374628258080
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
7.772 Γ— 10⁹²(93-digit number)
77720170555152909354…20213176374628258081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.554 Γ— 10⁹³(94-digit number)
15544034111030581870…40426352749256516161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.108 Γ— 10⁹³(94-digit number)
31088068222061163741…80852705498513032321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.217 Γ— 10⁹³(94-digit number)
62176136444122327483…61705410997026064641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.243 Γ— 10⁹⁴(95-digit number)
12435227288824465496…23410821994052129281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.487 Γ— 10⁹⁴(95-digit number)
24870454577648930993…46821643988104258561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.974 Γ— 10⁹⁴(95-digit number)
49740909155297861986…93643287976208517121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.948 Γ— 10⁹⁴(95-digit number)
99481818310595723973…87286575952417034241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.989 Γ— 10⁹⁡(96-digit number)
19896363662119144794…74573151904834068481
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 174027

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 5e355da737ca9982008f80454fa3479ff5d087b2708f2862b13f15c55724e2e8

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 #174,027 on Chainz β†—
Circulating Supply:57,861,931 XPMΒ·at block #6,827,228 Β· updates every 60s
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