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Block #175,720

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2013, 11:48:54 AM Β· Difficulty 9.8641 Β· 6,634,197 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
85ecc013f147f64f4d144f9ef1f62caf04d303e08fe7bb4136f2b0d917d31d33
View on Chainz β†—

Height

#175,720

Difficulty

9.864109

Transactions

1

Size

199 B

Version

2

Bits

09dd363f

Nonce

268,858

Timestamp

9/22/2013, 11:48:54 AM

Confirmations

6,634,197

Mined by

⛏️ P2SHAMFkKVcbthYfybM21VeAqtSFS6jCF37NqX

Merkle Root

58aa152e49f5e1e58b41bcd44bb92adfe1bd9881f9f44908677342c3994c0ef5
Transactions (1)
Coinbase58aa152e49f5e1…7342c3994c0ef5
1 in β†’ 1 out10.2600 XPM109 B
AMFkKVcb…jCF37NqX
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.

3.461 Γ— 10⁹⁡(96-digit number)
34610676612579021343…46343067447608474999
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.461 Γ— 10⁹⁡(96-digit number)
34610676612579021343…46343067447608474999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.922 Γ— 10⁹⁡(96-digit number)
69221353225158042687…92686134895216949999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.384 Γ— 10⁹⁢(97-digit number)
13844270645031608537…85372269790433899999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.768 Γ— 10⁹⁢(97-digit number)
27688541290063217075…70744539580867799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.537 Γ— 10⁹⁢(97-digit number)
55377082580126434150…41489079161735599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁷(98-digit number)
11075416516025286830…82978158323471199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.215 Γ— 10⁹⁷(98-digit number)
22150833032050573660…65956316646942399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.430 Γ— 10⁹⁷(98-digit number)
44301666064101147320…31912633293884799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.860 Γ— 10⁹⁷(98-digit number)
88603332128202294640…63825266587769599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁸(99-digit number)
17720666425640458928…27650533175539199999
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,723,421 XPMΒ·at block #6,809,916 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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