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Block #280,380

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/28/2013, 4:11:11 PM Β· Difficulty 9.9744 Β· 6,534,628 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
51c8fbae0e3731fbc576355e7ebaf9d863979f8a577c26964dd7a61cb250c6f7
View on Chainz β†—

Height

#280,380

Difficulty

9.974370

Transactions

1

Size

207 B

Version

2

Bits

09f97055

Nonce

8,221

Timestamp

11/28/2013, 4:11:11 PM

Confirmations

6,534,628

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

29ef57f6e505cd9c0fd6f334046847ba89f91375a172dd0ed20f26bb64bca868
Transactions (1)
Coinbase29ef57f6e505cd…0f26bb64bca868
1 in β†’ 1 out10.0400 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.318 Γ— 10⁹⁸(99-digit number)
23183584521434409661…80058671493678036799
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
2.318 Γ— 10⁹⁸(99-digit number)
23183584521434409661…80058671493678036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.636 Γ— 10⁹⁸(99-digit number)
46367169042868819323…60117342987356073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.273 Γ— 10⁹⁸(99-digit number)
92734338085737638646…20234685974712147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.854 Γ— 10⁹⁹(100-digit number)
18546867617147527729…40469371949424294399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.709 Γ— 10⁹⁹(100-digit number)
37093735234295055458…80938743898848588799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.418 Γ— 10⁹⁹(100-digit number)
74187470468590110917…61877487797697177599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.483 Γ— 10¹⁰⁰(101-digit number)
14837494093718022183…23754975595394355199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.967 Γ— 10¹⁰⁰(101-digit number)
29674988187436044366…47509951190788710399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.934 Γ— 10¹⁰⁰(101-digit number)
59349976374872088733…95019902381577420799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.186 Γ— 10¹⁰¹(102-digit number)
11869995274974417746…90039804763154841599
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:57,764,152 XPMΒ·at block #6,815,007 Β· updates every 60s
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