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Block #225,419

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/24/2013, 11:36:13 AM Β· Difficulty 9.9367 Β· 6,569,143 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ab42cf535f798818a8b5ddb94e03081425a42d3d671e2e3e66fb9cb9711ffb9
View on Chainz β†—

Height

#225,419

Difficulty

9.936661

Transactions

2

Size

539 B

Version

2

Bits

09efc905

Nonce

142,839

Timestamp

10/24/2013, 11:36:13 AM

Confirmations

6,569,143

Mined by

⛏️ P2SHANCqksLoVqiR7hPqU5yzcESxcMJs1ag8U2

Merkle Root

a868ef29a732a99e17ee3b25265b6d525d03c3656addd54bfdba90dca6551d92
Transactions (2)
Coinbase08ffeb9c9bfc4a…110ca46ee780a1
1 in β†’ 1 out10.1200 XPM109 B
ANCqksLo…Js1ag8U2
4ac3531a3f41c5…8be7e15dd839f3
2 in β†’ 1 out18.0534 XPM340 B
AVP1jJPw…gBdVxBxs
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.

8.155 Γ— 10⁹⁴(95-digit number)
81559372232083063019…86355269196408069119
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
8.155 Γ— 10⁹⁴(95-digit number)
81559372232083063019…86355269196408069119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.631 Γ— 10⁹⁡(96-digit number)
16311874446416612603…72710538392816138239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.262 Γ— 10⁹⁡(96-digit number)
32623748892833225207…45421076785632276479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.524 Γ— 10⁹⁡(96-digit number)
65247497785666450415…90842153571264552959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.304 Γ— 10⁹⁢(97-digit number)
13049499557133290083…81684307142529105919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.609 Γ— 10⁹⁢(97-digit number)
26098999114266580166…63368614285058211839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.219 Γ— 10⁹⁢(97-digit number)
52197998228533160332…26737228570116423679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.043 Γ— 10⁹⁷(98-digit number)
10439599645706632066…53474457140232847359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.087 Γ— 10⁹⁷(98-digit number)
20879199291413264133…06948914280465694719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.175 Γ— 10⁹⁷(98-digit number)
41758398582826528266…13897828560931389439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,600,539 XPMΒ·at block #6,794,561 Β· updates every 60s
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