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Block #264,694

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2013, 10:17:24 PM Β· Difficulty 9.9639 Β· 6,538,377 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
11874de367273a35a0181a1b2f18b2e35d9935f654b84e50be0ca91fab83e19d
View on Chainz β†—

Height

#264,694

Difficulty

9.963904

Transactions

1

Size

198 B

Version

2

Bits

09f6c26b

Nonce

38,781

Timestamp

11/18/2013, 10:17:24 PM

Confirmations

6,538,377

Mined by

⛏️ P2SHAdfhvjMUzrv47eGPURwcELGv4J3bm3edck

Merkle Root

06447080c6493f66ae8b0fc4f1783eb038cc0e76c06900ecc523c9b51498694c
Transactions (1)
Coinbase06447080c6493f…23c9b51498694c
1 in β†’ 1 out10.0600 XPM109 B
AdfhvjMU…3bm3edck
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.

1.998 Γ— 10⁹²(93-digit number)
19980215404112994974…30967698612302259601
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
1.998 Γ— 10⁹²(93-digit number)
19980215404112994974…30967698612302259601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.996 Γ— 10⁹²(93-digit number)
39960430808225989948…61935397224604519201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.992 Γ— 10⁹²(93-digit number)
79920861616451979896…23870794449209038401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.598 Γ— 10⁹³(94-digit number)
15984172323290395979…47741588898418076801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.196 Γ— 10⁹³(94-digit number)
31968344646580791958…95483177796836153601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.393 Γ— 10⁹³(94-digit number)
63936689293161583917…90966355593672307201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.278 Γ— 10⁹⁴(95-digit number)
12787337858632316783…81932711187344614401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.557 Γ— 10⁹⁴(95-digit number)
25574675717264633566…63865422374689228801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.114 Γ— 10⁹⁴(95-digit number)
51149351434529267133…27730844749378457601
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:57,668,597 XPMΒ·at block #6,803,070 Β· updates every 60s
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