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Block #288,377

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2013, 5:25:54 PM Β· Difficulty 9.9876 Β· 6,553,600 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6715fb7a3ec301bd777cfb2586516a6c781ab1a79cd7178ec38a3723982fae24
View on Chainz β†—

Height

#288,377

Difficulty

9.987644

Transactions

1

Size

208 B

Version

2

Bits

09fcd637

Nonce

6,889

Timestamp

12/1/2013, 5:25:54 PM

Confirmations

6,553,600

Merkle Root

94f462c8e3689dea448dcb97e9e7d7ac41f4833e2a7fc397bbf385e66584e70a
Transactions (1)
Coinbase94f462c8e3689d…f385e66584e70a
1 in β†’ 1 out10.0100 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.

1.422 Γ— 10⁹⁹(100-digit number)
14224257705657250862…01490580820675001600
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
1.422 Γ— 10⁹⁹(100-digit number)
14224257705657250862…01490580820675001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.844 Γ— 10⁹⁹(100-digit number)
28448515411314501724…02981161641350003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.689 Γ— 10⁹⁹(100-digit number)
56897030822629003449…05962323282700006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.137 Γ— 10¹⁰⁰(101-digit number)
11379406164525800689…11924646565400012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.275 Γ— 10¹⁰⁰(101-digit number)
22758812329051601379…23849293130800025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.551 Γ— 10¹⁰⁰(101-digit number)
45517624658103202759…47698586261600051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.103 Γ— 10¹⁰⁰(101-digit number)
91035249316206405519…95397172523200102401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.820 Γ— 10¹⁰¹(102-digit number)
18207049863241281103…90794345046400204801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.641 Γ— 10¹⁰¹(102-digit number)
36414099726482562207…81588690092800409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.282 Γ— 10¹⁰¹(102-digit number)
72828199452965124415…63177380185600819201
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 288377

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 6715fb7a3ec301bd777cfb2586516a6c781ab1a79cd7178ec38a3723982fae24

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 #288,377 on Chainz β†—
Circulating Supply:57,980,201 XPMΒ·at block #6,841,976 Β· updates every 60s
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