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Block #224,269

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/23/2013, 3:44:00 PM Β· Difficulty 9.9371 Β· 6,586,300 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2094b63eded138e51068cd4a5154e23c46173ba2380e350e47d77a321574332a
View on Chainz β†—

Height

#224,269

Difficulty

9.937129

Transactions

1

Size

198 B

Version

2

Bits

09efe7ac

Nonce

105,066

Timestamp

10/23/2013, 3:44:00 PM

Confirmations

6,586,300

Mined by

⛏️ P2SHAQVe2UA1iTQ9DYzoq3WAtRFrUDVMZmsiXq

Merkle Root

05d30a931fc980732bd86e2b08ab96eea8408b2992c888ba376fb3b7225251f5
Transactions (1)
Coinbase05d30a931fc980…6fb3b7225251f5
1 in β†’ 1 out10.1100 XPM109 B
AQVe2UA1…VMZmsiXq
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.

3.451 Γ— 10⁹²(93-digit number)
34513469129214988931…90744987444036997119
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
3.451 Γ— 10⁹²(93-digit number)
34513469129214988931…90744987444036997119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.902 Γ— 10⁹²(93-digit number)
69026938258429977863…81489974888073994239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.380 Γ— 10⁹³(94-digit number)
13805387651685995572…62979949776147988479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.761 Γ— 10⁹³(94-digit number)
27610775303371991145…25959899552295976959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.522 Γ— 10⁹³(94-digit number)
55221550606743982290…51919799104591953919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.104 Γ— 10⁹⁴(95-digit number)
11044310121348796458…03839598209183907839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.208 Γ— 10⁹⁴(95-digit number)
22088620242697592916…07679196418367815679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.417 Γ— 10⁹⁴(95-digit number)
44177240485395185832…15358392836735631359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.835 Γ— 10⁹⁴(95-digit number)
88354480970790371665…30716785673471262719
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:57,728,643 XPMΒ·at block #6,810,568 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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