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Block #173,373

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/20/2013, 10:35:05 PM Β· Difficulty 9.8609 Β· 6,670,085 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d99beaa3887f3fd4c4399eff71af0cfe13f8de5afeed14b4558546b9f54a9ede
View on Chainz β†—

Height

#173,373

Difficulty

9.860855

Transactions

2

Size

424 B

Version

2

Bits

09dc6106

Nonce

31,194

Timestamp

9/20/2013, 10:35:05 PM

Confirmations

6,670,085

Merkle Root

4f646bdb6fa59f3d06b6c0e5463432f21af306d7607037a6a73d9f442ee0b259
Transactions (2)
Coinbasee544b1cf36094a…9fa971478b6be8
1 in β†’ 1 out10.2800 XPM109 B
AYAZW9za…da8AvwiQ
66d38a5cf5281c…9cf3c7cc753055
1 in β†’ 2 out10.2400 XPM226 B
AYF9gzc3…CB765BZXALkVzNFi…6szjyZfb
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.

2.695 Γ— 10⁹³(94-digit number)
26955545009851317775…20262435113253123200
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
2.695 Γ— 10⁹³(94-digit number)
26955545009851317775…20262435113253123201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.391 Γ— 10⁹³(94-digit number)
53911090019702635550…40524870226506246401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.078 Γ— 10⁹⁴(95-digit number)
10782218003940527110…81049740453012492801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.156 Γ— 10⁹⁴(95-digit number)
21564436007881054220…62099480906024985601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.312 Γ— 10⁹⁴(95-digit number)
43128872015762108440…24198961812049971201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.625 Γ— 10⁹⁴(95-digit number)
86257744031524216880…48397923624099942401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.725 Γ— 10⁹⁡(96-digit number)
17251548806304843376…96795847248199884801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.450 Γ— 10⁹⁡(96-digit number)
34503097612609686752…93591694496399769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.900 Γ— 10⁹⁡(96-digit number)
69006195225219373504…87183388992799539201
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 173373

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 d99beaa3887f3fd4c4399eff71af0cfe13f8de5afeed14b4558546b9f54a9ede

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 #173,373 on Chainz β†—
Circulating Supply:57,992,032 XPMΒ·at block #6,843,457 Β· updates every 60s
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