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Block #223,301

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 9:46:59 PM Β· Difficulty 9.9384 Β· 6,583,259 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d2a608f9b02a960b2f82f4a6b86a046f7bfa65413cb5ed3d008e0c669637cd29
View on Chainz β†—

Height

#223,301

Difficulty

9.938440

Transactions

1

Size

199 B

Version

2

Bits

09f03d98

Nonce

133,539

Timestamp

10/22/2013, 9:46:59 PM

Confirmations

6,583,259

Mined by

⛏️ P2SHAKgiTbagke9hfkPB2Na9G5N62UMJA8ujWZ

Merkle Root

1f6e5012685fcc97b92ede10842a0fd93c03d7e8d31d6c9e91576be2b89d248d
Transactions (1)
Coinbase1f6e5012685fcc…576be2b89d248d
1 in β†’ 1 out10.1100 XPM109 B
AKgiTbag…MJA8ujWZ
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.

2.878 Γ— 10⁹⁡(96-digit number)
28784233694489871242…80724626309189406399
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
2.878 Γ— 10⁹⁡(96-digit number)
28784233694489871242…80724626309189406399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.756 Γ— 10⁹⁡(96-digit number)
57568467388979742485…61449252618378812799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁢(97-digit number)
11513693477795948497…22898505236757625599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.302 Γ— 10⁹⁢(97-digit number)
23027386955591896994…45797010473515251199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.605 Γ— 10⁹⁢(97-digit number)
46054773911183793988…91594020947030502399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.210 Γ— 10⁹⁢(97-digit number)
92109547822367587976…83188041894061004799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.842 Γ— 10⁹⁷(98-digit number)
18421909564473517595…66376083788122009599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.684 Γ— 10⁹⁷(98-digit number)
36843819128947035190…32752167576244019199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.368 Γ— 10⁹⁷(98-digit number)
73687638257894070380…65504335152488038399
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:57,696,576 XPMΒ·at block #6,806,559 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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