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Block #261,911

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/16/2013, 7:22:51 AM Β· Difficulty 9.9703 Β· 6,541,866 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1efbd9850d27873ba69b37b8c16c0ce232f6eed0b02b9ee339078a0660bba985
View on Chainz β†—

Height

#261,911

Difficulty

9.970271

Transactions

1

Size

199 B

Version

2

Bits

09f863ae

Nonce

248,985

Timestamp

11/16/2013, 7:22:51 AM

Confirmations

6,541,866

Mined by

⛏️ P2SHANYujwmo38BnnknbCyDhmsyWfuLhMeegnf

Merkle Root

bb50afe414515dae63d3051ff37c3cfa7d14b629f909609fd1e5ef971473b5a5
Transactions (1)
Coinbasebb50afe414515d…e5ef971473b5a5
1 in β†’ 1 out10.0400 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.

2.059 Γ— 10⁹⁡(96-digit number)
20592796374955038722…08618858414511283199
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
2.059 Γ— 10⁹⁡(96-digit number)
20592796374955038722…08618858414511283199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.118 Γ— 10⁹⁡(96-digit number)
41185592749910077444…17237716829022566399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.237 Γ— 10⁹⁡(96-digit number)
82371185499820154888…34475433658045132799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.647 Γ— 10⁹⁢(97-digit number)
16474237099964030977…68950867316090265599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.294 Γ— 10⁹⁢(97-digit number)
32948474199928061955…37901734632180531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.589 Γ— 10⁹⁢(97-digit number)
65896948399856123910…75803469264361062399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁷(98-digit number)
13179389679971224782…51606938528722124799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.635 Γ— 10⁹⁷(98-digit number)
26358779359942449564…03213877057444249599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.271 Γ— 10⁹⁷(98-digit number)
52717558719884899128…06427754114888499199
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:57,674,255 XPMΒ·at block #6,803,776 Β· updates every 60s
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