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Block #106,761

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2013, 4:23:47 AM Β· Difficulty 9.6150 Β· 6,723,734 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b33149893c0b084eebd7d5b6c3403666629d4926b0af6dc58cb17253bfd07fa9
View on Chainz β†—

Height

#106,761

Difficulty

9.615019

Transactions

1

Size

200 B

Version

2

Bits

099d71e8

Nonce

61,502

Timestamp

8/9/2013, 4:23:47 AM

Confirmations

6,723,734

Mined by

⛏️ P2SHARkKyc6864gXuGt7xaiNsFWc7sbXw8oqMc

Merkle Root

13e1a1a0ba40375cb0546e971781e572ba998020edacf2b57575446e77cf669d
Transactions (1)
Coinbase13e1a1a0ba4037…75446e77cf669d
1 in β†’ 1 out10.8000 XPM109 B
ARkKyc68…bXw8oqMc
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.

5.331 Γ— 10⁹⁢(97-digit number)
53311470431948302702…74155191682590565501
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
5.331 Γ— 10⁹⁢(97-digit number)
53311470431948302702…74155191682590565501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.066 Γ— 10⁹⁷(98-digit number)
10662294086389660540…48310383365181131001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.132 Γ— 10⁹⁷(98-digit number)
21324588172779321081…96620766730362262001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.264 Γ— 10⁹⁷(98-digit number)
42649176345558642162…93241533460724524001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.529 Γ— 10⁹⁷(98-digit number)
85298352691117284324…86483066921449048001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.705 Γ— 10⁹⁸(99-digit number)
17059670538223456864…72966133842898096001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.411 Γ— 10⁹⁸(99-digit number)
34119341076446913729…45932267685796192001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.823 Γ— 10⁹⁸(99-digit number)
68238682152893827459…91864535371592384001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.364 Γ— 10⁹⁹(100-digit number)
13647736430578765491…83729070743184768001
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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