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Block #208,403

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/13/2013, 11:49:44 PM Β· Difficulty 9.9063 Β· 6,595,122 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
76b9c24d6889056dbb337acf5f79b8366883c0916c3cbc46ae0c5467a6b48cc5
View on Chainz β†—

Height

#208,403

Difficulty

9.906294

Transactions

3

Size

993 B

Version

2

Bits

09e802de

Nonce

10,967

Timestamp

10/13/2013, 11:49:44 PM

Confirmations

6,595,122

Mined by

⛏️ P2SHANcX13Fk7xSX8wFr5zRphRpXHx1biNXNGx

Merkle Root

eed36b9f3da1aa0f896e62f5fa448972b11470ecab9cc5177491fe15933e2a02
Transactions (3)
Coinbasec5e5ff2f78ac3b…e4ead291f4c0fd
1 in β†’ 1 out10.1900 XPM109 B
ANcX13Fk…1biNXNGx
f0fec385433192…68da0059786d7d
1 in β†’ 2 out10.2000 XPM192 B
Acf39C89…aMDnU3XFATqUiTD6…rzaZ5G6Z
f728640f0cfe0b…7e759005225b29
4 in β†’ 2 out21.0300 XPM602 B
Acf39C89…aMDnU3XFAV9YRr9M…3tmE6qxm
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.

5.567 Γ— 10⁹⁡(96-digit number)
55673129387008765546…60718149631920057681
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
5.567 Γ— 10⁹⁡(96-digit number)
55673129387008765546…60718149631920057681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.113 Γ— 10⁹⁢(97-digit number)
11134625877401753109…21436299263840115361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.226 Γ— 10⁹⁢(97-digit number)
22269251754803506218…42872598527680230721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.453 Γ— 10⁹⁢(97-digit number)
44538503509607012437…85745197055360461441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.907 Γ— 10⁹⁢(97-digit number)
89077007019214024874…71490394110720922881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.781 Γ— 10⁹⁷(98-digit number)
17815401403842804974…42980788221441845761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.563 Γ— 10⁹⁷(98-digit number)
35630802807685609949…85961576442883691521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.126 Γ— 10⁹⁷(98-digit number)
71261605615371219899…71923152885767383041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.425 Γ— 10⁹⁸(99-digit number)
14252321123074243979…43846305771534766081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,672,227 XPMΒ·at block #6,803,524 Β· updates every 60s
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