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Block #209,341

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/14/2013, 12:54:22 PM Β· Difficulty 9.9092 Β· 6,617,368 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
819c7f7b102256dcbaa9fd4d600bc3bd8a812a8b33427c1ee373c033d2a560ff
View on Chainz β†—

Height

#209,341

Difficulty

9.909151

Transactions

1

Size

199 B

Version

2

Bits

09e8be1a

Nonce

39,744

Timestamp

10/14/2013, 12:54:22 PM

Confirmations

6,617,368

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

676fd3543502a805662c8cafcc3bb7429ee243ad69e5e686b28928d787e17713
Transactions (1)
Coinbase676fd3543502a8…8928d787e17713
1 in β†’ 1 out10.1700 XPM110 B
AbuU1HhS…JPwsJEbB
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.

3.086 Γ— 10⁹²(93-digit number)
30861361144061455041…13389508042523090401
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
3.086 Γ— 10⁹²(93-digit number)
30861361144061455041…13389508042523090401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.172 Γ— 10⁹²(93-digit number)
61722722288122910083…26779016085046180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.234 Γ— 10⁹³(94-digit number)
12344544457624582016…53558032170092361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.468 Γ— 10⁹³(94-digit number)
24689088915249164033…07116064340184723201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.937 Γ— 10⁹³(94-digit number)
49378177830498328066…14232128680369446401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.875 Γ— 10⁹³(94-digit number)
98756355660996656132…28464257360738892801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.975 Γ— 10⁹⁴(95-digit number)
19751271132199331226…56928514721477785601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.950 Γ— 10⁹⁴(95-digit number)
39502542264398662453…13857029442955571201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.900 Γ— 10⁹⁴(95-digit number)
79005084528797324906…27714058885911142401
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.

β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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, …
Cross-reference on Chainz Explorer
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