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Block #176,017

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2013, 4:38:46 PM Β· Difficulty 9.8643 Β· 6,626,653 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4061dd368066d8c5321fa5aaba7218c89decceb58dea242eb3d16a28c52f6577
View on Chainz β†—

Height

#176,017

Difficulty

9.864292

Transactions

1

Size

219 B

Version

2

Bits

09dd4239

Nonce

1,164,746,944

Timestamp

9/22/2013, 4:38:46 PM

Confirmations

6,626,653

Mined by

⛏️ R?>AGLpT5zBCy42ej8dmuMEVvxHoCBnHeFXQg

Merkle Root

cf9b3059b00872b60346197331f8fc7d8996653e41109deef3fa0f05e9efcb01
Transactions (1)
Coinbasecf9b3059b00872…fa0f05e9efcb01
1 in β†’ 2 out10.2600 XPM130 B
AGLpT5zB…BnHeFXQgAa25tiQt…Q336nrKS
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.

2.719 Γ— 10⁹²(93-digit number)
27197270619503041711…80346363879557626001
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
2.719 Γ— 10⁹²(93-digit number)
27197270619503041711…80346363879557626001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.439 Γ— 10⁹²(93-digit number)
54394541239006083423…60692727759115252001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.087 Γ— 10⁹³(94-digit number)
10878908247801216684…21385455518230504001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.175 Γ— 10⁹³(94-digit number)
21757816495602433369…42770911036461008001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.351 Γ— 10⁹³(94-digit number)
43515632991204866738…85541822072922016001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.703 Γ— 10⁹³(94-digit number)
87031265982409733477…71083644145844032001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.740 Γ— 10⁹⁴(95-digit number)
17406253196481946695…42167288291688064001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.481 Γ— 10⁹⁴(95-digit number)
34812506392963893390…84334576583376128001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.962 Γ— 10⁹⁴(95-digit number)
69625012785927786781…68669153166752256001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.392 Γ— 10⁹⁡(96-digit number)
13925002557185557356…37338306333504512001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,665,380 XPMΒ·at block #6,802,669 Β· updates every 60s
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