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Block #139,973

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2013, 8:54:58 AM Β· Difficulty 9.8318 Β· 6,674,415 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
30bed7733a5515b08091d8f1a6160b4730ec0dc82776b7f9d17fb6aa39067957
View on Chainz β†—

Height

#139,973

Difficulty

9.831776

Transactions

1

Size

199 B

Version

2

Bits

09d4ef4c

Nonce

7,367

Timestamp

8/29/2013, 8:54:58 AM

Confirmations

6,674,415

Mined by

⛏️ P2SHAKVWeAriNw95pyvDwPjKdiw6WPDCVyQ7Tr

Merkle Root

1338ef8ba0fac8a172997c9cd1ec971286b6dbc8065e3e654a1b6ac7f8888c0a
Transactions (1)
Coinbase1338ef8ba0fac8…1b6ac7f8888c0a
1 in β†’ 1 out10.3300 XPM109 B
AKVWeAri…DCVyQ7Tr
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.

8.287 Γ— 10⁹³(94-digit number)
82875568902510555326…15329234394847818721
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
8.287 Γ— 10⁹³(94-digit number)
82875568902510555326…15329234394847818721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.657 Γ— 10⁹⁴(95-digit number)
16575113780502111065…30658468789695637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.315 Γ— 10⁹⁴(95-digit number)
33150227561004222130…61316937579391274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.630 Γ— 10⁹⁴(95-digit number)
66300455122008444261…22633875158782549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.326 Γ— 10⁹⁡(96-digit number)
13260091024401688852…45267750317565099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.652 Γ— 10⁹⁡(96-digit number)
26520182048803377704…90535500635130199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.304 Γ— 10⁹⁡(96-digit number)
53040364097606755409…81071001270260398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.060 Γ— 10⁹⁢(97-digit number)
10608072819521351081…62142002540520796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.121 Γ— 10⁹⁢(97-digit number)
21216145639042702163…24284005081041592321
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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