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Block #268,709

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/22/2013, 8:31:03 AM Β· Difficulty 9.9569 Β· 6,535,068 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1d44a10e6c88b8bc38655985a2c3ccf37387b1a8340c10fc0174800792e4a27e
View on Chainz β†—

Height

#268,709

Difficulty

9.956865

Transactions

1

Size

198 B

Version

2

Bits

09f4f51b

Nonce

67,191

Timestamp

11/22/2013, 8:31:03 AM

Confirmations

6,535,068

Mined by

⛏️ P2SHANYujwmo38BnnknbCyDhmsyWfuLhMeegnf

Merkle Root

ed5fe3c6d2954e26112462af6843e5ae7e6a096522ad715e5f102a108d32cbc8
Transactions (1)
Coinbaseed5fe3c6d2954e…102a108d32cbc8
1 in β†’ 1 out10.0700 XPM109 B
ANYujwmo…LhMeegnf
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.

1.867 Γ— 10⁹³(94-digit number)
18678243586194409153…11013087986845098041
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
1.867 Γ— 10⁹³(94-digit number)
18678243586194409153…11013087986845098041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.735 Γ— 10⁹³(94-digit number)
37356487172388818307…22026175973690196081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.471 Γ— 10⁹³(94-digit number)
74712974344777636615…44052351947380392161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.494 Γ— 10⁹⁴(95-digit number)
14942594868955527323…88104703894760784321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.988 Γ— 10⁹⁴(95-digit number)
29885189737911054646…76209407789521568641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.977 Γ— 10⁹⁴(95-digit number)
59770379475822109292…52418815579043137281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.195 Γ— 10⁹⁡(96-digit number)
11954075895164421858…04837631158086274561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.390 Γ— 10⁹⁡(96-digit number)
23908151790328843717…09675262316172549121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.781 Γ— 10⁹⁡(96-digit number)
47816303580657687434…19350524632345098241
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
Circulating Supply:57,674,255 XPMΒ·at block #6,803,776 Β· updates every 60s
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