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Block #225,269

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/24/2013, 9:10:53 AM Β· Difficulty 9.9366 Β· 6,585,068 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c110ec9ae196d5e39c6433329d7fcc6cdce05c8c8b6f35d5499e50cb192b61d1
View on Chainz β†—

Height

#225,269

Difficulty

9.936584

Transactions

1

Size

199 B

Version

2

Bits

09efc3f6

Nonce

3,209

Timestamp

10/24/2013, 9:10:53 AM

Confirmations

6,585,068

Mined by

⛏️ P2SHALC2Be3ybZodrnZHemHj8exXk9kpW3tbSE

Merkle Root

756abafeabf2652e80cfd4106a657cefe0c3ad46da75b55b61005576728c495d
Transactions (1)
Coinbase756abafeabf265…005576728c495d
1 in β†’ 1 out10.1100 XPM109 B
ALC2Be3y…kpW3tbSE
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.

2.699 Γ— 10⁹⁴(95-digit number)
26997112544104482035…38394073902863365119
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
2.699 Γ— 10⁹⁴(95-digit number)
26997112544104482035…38394073902863365119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.399 Γ— 10⁹⁴(95-digit number)
53994225088208964071…76788147805726730239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.079 Γ— 10⁹⁡(96-digit number)
10798845017641792814…53576295611453460479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.159 Γ— 10⁹⁡(96-digit number)
21597690035283585628…07152591222906920959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.319 Γ— 10⁹⁡(96-digit number)
43195380070567171257…14305182445813841919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.639 Γ— 10⁹⁡(96-digit number)
86390760141134342514…28610364891627683839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.727 Γ— 10⁹⁢(97-digit number)
17278152028226868502…57220729783255367679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.455 Γ— 10⁹⁢(97-digit number)
34556304056453737005…14441459566510735359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.911 Γ— 10⁹⁢(97-digit number)
69112608112907474011…28882919133021470719
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:57,726,777 XPMΒ·at block #6,810,336 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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