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Block #230,425

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/27/2013, 7:29:12 PM Β· Difficulty 9.9395 Β· 6,572,277 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea567b3996c346bd0d27be8bad0323e6fdc8f45978415cd9ca53efc9e3150fbb
View on Chainz β†—

Height

#230,425

Difficulty

9.939481

Transactions

1

Size

198 B

Version

2

Bits

09f081d8

Nonce

5,631

Timestamp

10/27/2013, 7:29:12 PM

Confirmations

6,572,277

Mined by

⛏️ P2SHAbERMcutQDScg9DXkU4LAqx7CDQQKtkzeK

Merkle Root

f3beb65c9089380c9c028d9a8a7e9b560cbf0db8b2cce1dcb4e5fb40dd1a2fed
Transactions (1)
Coinbasef3beb65c908938…e5fb40dd1a2fed
1 in β†’ 1 out10.1100 XPM109 B
AbERMcut…QQKtkzeK
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.

4.841 Γ— 10⁹²(93-digit number)
48419987413358869183…00679552463141027199
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
4.841 Γ— 10⁹²(93-digit number)
48419987413358869183…00679552463141027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.683 Γ— 10⁹²(93-digit number)
96839974826717738366…01359104926282054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.936 Γ— 10⁹³(94-digit number)
19367994965343547673…02718209852564108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.873 Γ— 10⁹³(94-digit number)
38735989930687095346…05436419705128217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.747 Γ— 10⁹³(94-digit number)
77471979861374190693…10872839410256435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.549 Γ— 10⁹⁴(95-digit number)
15494395972274838138…21745678820512870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.098 Γ— 10⁹⁴(95-digit number)
30988791944549676277…43491357641025740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.197 Γ— 10⁹⁴(95-digit number)
61977583889099352554…86982715282051481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.239 Γ— 10⁹⁡(96-digit number)
12395516777819870510…73965430564102963199
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:57,665,641 XPMΒ·at block #6,802,701 Β· updates every 60s
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