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Block #178,010

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/24/2013, 2:37:17 AM Β· Difficulty 9.8632 Β· 6,646,667 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d67245accd7843ffcae6fe526cafbda8e56bc4e18770eb75f866d5c38d80bac4
View on Chainz β†—

Height

#178,010

Difficulty

9.863185

Transactions

1

Size

200 B

Version

2

Bits

09dcf9b3

Nonce

211,805

Timestamp

9/24/2013, 2:37:17 AM

Confirmations

6,646,667

Merkle Root

ac852f9cfafb5c71fc714695c0d7059e713496f07a48b6af96f63d5b5d43277a
Transactions (1)
Coinbaseac852f9cfafb5c…f63d5b5d43277a
1 in β†’ 1 out10.2600 XPM109 B
AbpE9nDN…P1CH6zzP
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.

9.025 Γ— 10⁹⁢(97-digit number)
90253465978568097444…65894614281170159060
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
9.025 Γ— 10⁹⁢(97-digit number)
90253465978568097444…65894614281170159061
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.805 Γ— 10⁹⁷(98-digit number)
18050693195713619488…31789228562340318121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.610 Γ— 10⁹⁷(98-digit number)
36101386391427238977…63578457124680636241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.220 Γ— 10⁹⁷(98-digit number)
72202772782854477955…27156914249361272481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.444 Γ— 10⁹⁸(99-digit number)
14440554556570895591…54313828498722544961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.888 Γ— 10⁹⁸(99-digit number)
28881109113141791182…08627656997445089921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.776 Γ— 10⁹⁸(99-digit number)
57762218226283582364…17255313994890179841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.155 Γ— 10⁹⁹(100-digit number)
11552443645256716472…34510627989780359681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.310 Γ— 10⁹⁹(100-digit number)
23104887290513432945…69021255979560719361
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 178010

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 d67245accd7843ffcae6fe526cafbda8e56bc4e18770eb75f866d5c38d80bac4

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 #178,010 on Chainz β†—
Circulating Supply:57,841,480 XPMΒ·at block #6,824,676 Β· updates every 60s
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