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Block #30,430

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/13/2013, 7:05:11 PM Β· Difficulty 7.9869 Β· 6,794,908 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c71ce1c8aea6ff2e803de0075e4735c160ba58b983bb4f7f047adc6b3ecbbd6e
View on Chainz β†—

Height

#30,430

Difficulty

7.986852

Transactions

1

Size

195 B

Version

2

Bits

07fca24f

Nonce

377

Timestamp

7/13/2013, 7:05:11 PM

Confirmations

6,794,908

Mined by

⛏️ P2SHAXciC8HNS9S5P5rEuP4DvtNMFMEX3Zpc3u

Merkle Root

878d81c5594bc5f657763a13fee44c075ecb4fec4a5ef6d7963f96180b0b410d
Transactions (1)
Coinbase878d81c5594bc5…3f96180b0b410d
1 in β†’ 1 out15.6600 XPM108 B
AXciC8HN…EX3Zpc3u
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.

2.196 Γ— 10⁸⁷(88-digit number)
21967605177382007683…67925581523391375239
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
2.196 Γ— 10⁸⁷(88-digit number)
21967605177382007683…67925581523391375239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.393 Γ— 10⁸⁷(88-digit number)
43935210354764015367…35851163046782750479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.787 Γ— 10⁸⁷(88-digit number)
87870420709528030735…71702326093565500959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.757 Γ— 10⁸⁸(89-digit number)
17574084141905606147…43404652187131001919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.514 Γ— 10⁸⁸(89-digit number)
35148168283811212294…86809304374262003839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.029 Γ— 10⁸⁸(89-digit number)
70296336567622424588…73618608748524007679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.405 Γ— 10⁸⁹(90-digit number)
14059267313524484917…47237217497048015359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.811 Γ— 10⁸⁹(90-digit number)
28118534627048969835…94474434994096030719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,846,808 XPMΒ·at block #6,825,337 Β· updates every 60s
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