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Block #104,896

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/8/2013, 6:38:19 AM Β· Difficulty 9.5695 Β· 6,711,139 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5c9dcb7fad725b34904aba0ea71d9a5f34d07da2de2c5746be0e0ac1df99d7d
View on Chainz β†—

Height

#104,896

Difficulty

9.569541

Transactions

1

Size

201 B

Version

2

Bits

0991cd77

Nonce

76,332

Timestamp

8/8/2013, 6:38:19 AM

Confirmations

6,711,139

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

16d078fda57c461b27e36f2b927e2ec42d6a4e34d2c8bfc01d613077f4f97fb5
Transactions (1)
Coinbase16d078fda57c46…613077f4f97fb5
1 in β†’ 1 out10.9000 XPM109 B
AXvMMum1…y1ajpFRb
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.

5.694 Γ— 10⁹⁸(99-digit number)
56946886073295250603…10030859228309186461
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
5.694 Γ— 10⁹⁸(99-digit number)
56946886073295250603…10030859228309186461
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.138 Γ— 10⁹⁹(100-digit number)
11389377214659050120…20061718456618372921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.277 Γ— 10⁹⁹(100-digit number)
22778754429318100241…40123436913236745841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.555 Γ— 10⁹⁹(100-digit number)
45557508858636200483…80246873826473491681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.111 Γ— 10⁹⁹(100-digit number)
91115017717272400966…60493747652946983361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.822 Γ— 10¹⁰⁰(101-digit number)
18223003543454480193…20987495305893966721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.644 Γ— 10¹⁰⁰(101-digit number)
36446007086908960386…41974990611787933441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.289 Γ— 10¹⁰⁰(101-digit number)
72892014173817920772…83949981223575866881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.457 Γ— 10¹⁰¹(102-digit number)
14578402834763584154…67899962447151733761
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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