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Block #230,988

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/28/2013, 3:56:55 AM Β· Difficulty 9.9402 Β· 6,586,300 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7babd75316eb07aca54d2ad4b52cb3bb0c8f9557573ae20db5fcd8abbd96f7fd
View on Chainz β†—

Height

#230,988

Difficulty

9.940159

Transactions

1

Size

200 B

Version

2

Bits

09f0ae42

Nonce

34,329

Timestamp

10/28/2013, 3:56:55 AM

Confirmations

6,586,300

Mined by

⛏️ P2SHAMH15paJo2oDg3nSMDKhRnzJSxXd9hymDS

Merkle Root

9c243c96334855e4378c800b6bd50635364c3455a1c8d7e56b40b9db99b0c6ad
Transactions (1)
Coinbase9c243c96334855…40b9db99b0c6ad
1 in β†’ 1 out10.1100 XPM109 B
AMH15paJ…Xd9hymDS
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.

4.473 Γ— 10⁹⁷(98-digit number)
44737585531968960166…54688934633373268001
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
4.473 Γ— 10⁹⁷(98-digit number)
44737585531968960166…54688934633373268001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.947 Γ— 10⁹⁷(98-digit number)
89475171063937920332…09377869266746536001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.789 Γ— 10⁹⁸(99-digit number)
17895034212787584066…18755738533493072001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.579 Γ— 10⁹⁸(99-digit number)
35790068425575168133…37511477066986144001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.158 Γ— 10⁹⁸(99-digit number)
71580136851150336266…75022954133972288001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.431 Γ— 10⁹⁹(100-digit number)
14316027370230067253…50045908267944576001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.863 Γ— 10⁹⁹(100-digit number)
28632054740460134506…00091816535889152001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.726 Γ— 10⁹⁹(100-digit number)
57264109480920269013…00183633071778304001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.145 Γ— 10¹⁰⁰(101-digit number)
11452821896184053802…00367266143556608001
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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