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Block #192,083

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/3/2013, 3:02:08 PM Β· Difficulty 9.8747 Β· 6,624,226 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c4aa21adc435c764e3f6142f291c6fa1e1fb8d53c3a31b8e0ef5a6f81662dc7
View on Chainz β†—

Height

#192,083

Difficulty

9.874732

Transactions

1

Size

200 B

Version

2

Bits

09dfee76

Nonce

17,853

Timestamp

10/3/2013, 3:02:08 PM

Confirmations

6,624,226

Mined by

⛏️ P2SHAPK6TsLc8JxWgj41xMVz2y8mnfkbATRbnm

Merkle Root

4db8f62b82d351909db2869b394f9dd75085f41e485bdacdc603ef72e9cf986a
Transactions (1)
Coinbase4db8f62b82d351…03ef72e9cf986a
1 in β†’ 1 out10.2400 XPM109 B
APK6TsLc…kbATRbnm
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.

9.775 Γ— 10⁹⁡(96-digit number)
97750331821918813404…62512086943799920001
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
9.775 Γ— 10⁹⁡(96-digit number)
97750331821918813404…62512086943799920001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.955 Γ— 10⁹⁢(97-digit number)
19550066364383762680…25024173887599840001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.910 Γ— 10⁹⁢(97-digit number)
39100132728767525361…50048347775199680001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.820 Γ— 10⁹⁢(97-digit number)
78200265457535050723…00096695550399360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.564 Γ— 10⁹⁷(98-digit number)
15640053091507010144…00193391100798720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.128 Γ— 10⁹⁷(98-digit number)
31280106183014020289…00386782201597440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.256 Γ— 10⁹⁷(98-digit number)
62560212366028040578…00773564403194880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.251 Γ— 10⁹⁸(99-digit number)
12512042473205608115…01547128806389760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.502 Γ— 10⁹⁸(99-digit number)
25024084946411216231…03094257612779520001
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
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