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Block #193,203

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/4/2013, 9:06:09 AM Β· Difficulty 9.8758 Β· 6,623,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
18a16a1700307a93372d23e101bda185b701b78bd6fc11e812c95e8a56378369
View on Chainz β†—

Height

#193,203

Difficulty

9.875770

Transactions

1

Size

199 B

Version

2

Bits

09e03278

Nonce

32,923

Timestamp

10/4/2013, 9:06:09 AM

Confirmations

6,623,045

Mined by

⛏️ P2SHAMjEL5jU5FrR33MFDHGMbVsnwkXWAbZRhp

Merkle Root

1d28a1dbd30af90d830f4d537b216ab07afcf1b8e0f7e12ffa2c6f8107baaf2a
Transactions (1)
Coinbase1d28a1dbd30af9…2c6f8107baaf2a
1 in β†’ 1 out10.2400 XPM109 B
AMjEL5jU…XWAbZRhp
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.

7.948 Γ— 10⁹⁴(95-digit number)
79484525526699545169…55987305478304776001
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
7.948 Γ— 10⁹⁴(95-digit number)
79484525526699545169…55987305478304776001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.589 Γ— 10⁹⁡(96-digit number)
15896905105339909033…11974610956609552001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.179 Γ— 10⁹⁡(96-digit number)
31793810210679818067…23949221913219104001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.358 Γ— 10⁹⁡(96-digit number)
63587620421359636135…47898443826438208001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.271 Γ— 10⁹⁢(97-digit number)
12717524084271927227…95796887652876416001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.543 Γ— 10⁹⁢(97-digit number)
25435048168543854454…91593775305752832001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.087 Γ— 10⁹⁢(97-digit number)
50870096337087708908…83187550611505664001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.017 Γ— 10⁹⁷(98-digit number)
10174019267417541781…66375101223011328001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.034 Γ— 10⁹⁷(98-digit number)
20348038534835083563…32750202446022656001
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:57,774,103 XPMΒ·at block #6,816,247 Β· updates every 60s
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