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Block #203,420

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/10/2013, 8:12:30 PM Β· Difficulty 9.8974 Β· 6,623,735 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e80521119ef843e338da17278e01b60b169b8e0834f54ad8c35d135940f3662b
View on Chainz β†—

Height

#203,420

Difficulty

9.897376

Transactions

1

Size

198 B

Version

2

Bits

09e5ba6e

Nonce

137,359

Timestamp

10/10/2013, 8:12:30 PM

Confirmations

6,623,735

Mined by

⛏️ P2SHAbJUC2oSrZY84nuu7WUoHPgJjAcpKam6LK

Merkle Root

91b0b067ad9e8b92f08eed9e64feba6a0bd4d87b21034c007608eee05ff8d7ee
Transactions (1)
Coinbase91b0b067ad9e8b…08eee05ff8d7ee
1 in β†’ 1 out10.1900 XPM109 B
AbJUC2oS…cpKam6LK
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.

1.770 Γ— 10⁹³(94-digit number)
17708693482178100927…30974250776116989439
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
1.770 Γ— 10⁹³(94-digit number)
17708693482178100927…30974250776116989439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.541 Γ— 10⁹³(94-digit number)
35417386964356201855…61948501552233978879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.083 Γ— 10⁹³(94-digit number)
70834773928712403711…23897003104467957759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.416 Γ— 10⁹⁴(95-digit number)
14166954785742480742…47794006208935915519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.833 Γ— 10⁹⁴(95-digit number)
28333909571484961484…95588012417871831039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.666 Γ— 10⁹⁴(95-digit number)
56667819142969922969…91176024835743662079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.133 Γ— 10⁹⁡(96-digit number)
11333563828593984593…82352049671487324159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.266 Γ— 10⁹⁡(96-digit number)
22667127657187969187…64704099342974648319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.533 Γ— 10⁹⁡(96-digit number)
45334255314375938375…29408198685949296639
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:57,861,424 XPMΒ·at block #6,827,154 Β· updates every 60s
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