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Block #265,426

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/19/2013, 1:30:33 PM Β· Difficulty 9.9626 Β· 6,577,410 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e85f4d3719dda2515904774d9c9a10a35bd5d1d3091da350ecef33558c27aca3
View on Chainz β†—

Height

#265,426

Difficulty

9.962624

Transactions

1

Size

208 B

Version

2

Bits

09f66e83

Nonce

134

Timestamp

11/19/2013, 1:30:33 PM

Confirmations

6,577,410

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

634686722172369f9acf65e14fa7495a5d4ff229d7ebc0f4f6aafc1887dcf006
Transactions (1)
Coinbase63468672217236…aafc1887dcf006
1 in β†’ 1 out10.0600 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.

4.395 Γ— 10⁹⁸(99-digit number)
43959488829155714579…70930245161144962499
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.395 Γ— 10⁹⁸(99-digit number)
43959488829155714579…70930245161144962499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.791 Γ— 10⁹⁸(99-digit number)
87918977658311429158…41860490322289924999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁹(100-digit number)
17583795531662285831…83720980644579849999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.516 Γ— 10⁹⁹(100-digit number)
35167591063324571663…67441961289159699999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.033 Γ— 10⁹⁹(100-digit number)
70335182126649143326…34883922578319399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.406 Γ— 10¹⁰⁰(101-digit number)
14067036425329828665…69767845156638799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.813 Γ— 10¹⁰⁰(101-digit number)
28134072850659657330…39535690313277599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.626 Γ— 10¹⁰⁰(101-digit number)
56268145701319314661…79071380626555199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.125 Γ— 10¹⁰¹(102-digit number)
11253629140263862932…58142761253110399999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,987,032 XPMΒ·at block #6,842,835 Β· updates every 60s
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