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Block #113,076

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2013, 8:22:00 AM Β· Difficulty 9.7285 Β· 6,682,372 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7c17798d01410e3e8ac2aaa1b8f8a8dde4fe803131b8fdbc9ba6faa063345944
View on Chainz β†—

Height

#113,076

Difficulty

9.728539

Transactions

1

Size

200 B

Version

2

Bits

09ba8186

Nonce

303,680

Timestamp

8/12/2013, 8:22:00 AM

Confirmations

6,682,372

Mined by

⛏️ P2SHAdhmaJ1p1gqeX3dfcHueRxnjGJMhFRDjQ7

Merkle Root

f4c7b56572bccef69328c66eb2aa2cb05687b199ea22a143764a52a6ccfd97d0
Transactions (1)
Coinbasef4c7b56572bcce…4a52a6ccfd97d0
1 in β†’ 1 out10.5500 XPM109 B
AdhmaJ1p…MhFRDjQ7
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.

1.555 Γ— 10⁹⁸(99-digit number)
15559888342067800041…31306779152741282079
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
1.555 Γ— 10⁹⁸(99-digit number)
15559888342067800041…31306779152741282079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.111 Γ— 10⁹⁸(99-digit number)
31119776684135600082…62613558305482564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.223 Γ— 10⁹⁸(99-digit number)
62239553368271200164…25227116610965128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.244 Γ— 10⁹⁹(100-digit number)
12447910673654240032…50454233221930256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.489 Γ— 10⁹⁹(100-digit number)
24895821347308480065…00908466443860513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.979 Γ— 10⁹⁹(100-digit number)
49791642694616960131…01816932887721026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.958 Γ— 10⁹⁹(100-digit number)
99583285389233920263…03633865775442053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.991 Γ— 10¹⁰⁰(101-digit number)
19916657077846784052…07267731550884106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.983 Γ— 10¹⁰⁰(101-digit number)
39833314155693568105…14535463101768212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.966 Γ— 10¹⁰⁰(101-digit number)
79666628311387136210…29070926203536424959
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:57,607,649 XPMΒ·at block #6,795,447 Β· updates every 60s
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