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Block #235,280

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/30/2013, 8:09:51 PM Β· Difficulty 9.9454 Β· 6,568,497 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c876be79085d59c18dabe6ea046cd07b36e4a19776c5c542b7ec977793d5eded
View on Chainz β†—

Height

#235,280

Difficulty

9.945368

Transactions

1

Size

199 B

Version

2

Bits

09f2039d

Nonce

568,015

Timestamp

10/30/2013, 8:09:51 PM

Confirmations

6,568,497

Mined by

⛏️ P2SHANYujwmo38BnnknbCyDhmsyWfuLhMeegnf

Merkle Root

eeeeb3ed681cca68be6b40de7a4e4101958391475aa03421ebfde43966e9e76d
Transactions (1)
Coinbaseeeeeb3ed681cca…fde43966e9e76d
1 in β†’ 1 out10.1000 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.

1.212 Γ— 10⁹⁡(96-digit number)
12129557519394429838…29415368911320145999
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
1.212 Γ— 10⁹⁡(96-digit number)
12129557519394429838…29415368911320145999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.425 Γ— 10⁹⁡(96-digit number)
24259115038788859677…58830737822640291999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.851 Γ— 10⁹⁡(96-digit number)
48518230077577719355…17661475645280583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.703 Γ— 10⁹⁡(96-digit number)
97036460155155438711…35322951290561167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.940 Γ— 10⁹⁢(97-digit number)
19407292031031087742…70645902581122335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.881 Γ— 10⁹⁢(97-digit number)
38814584062062175484…41291805162244671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.762 Γ— 10⁹⁢(97-digit number)
77629168124124350969…82583610324489343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.552 Γ— 10⁹⁷(98-digit number)
15525833624824870193…65167220648978687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.105 Γ— 10⁹⁷(98-digit number)
31051667249649740387…30334441297957375999
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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