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Block #207,228

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/13/2013, 8:10:29 AM Β· Difficulty 9.9018 Β· 6,601,653 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1c49b03f1fe692cf0ce523ebe0f91789f59c7305ee54831f82de44ac8ac930da
View on Chainz β†—

Height

#207,228

Difficulty

9.901751

Transactions

1

Size

197 B

Version

2

Bits

09e6d92a

Nonce

83,980

Timestamp

10/13/2013, 8:10:29 AM

Confirmations

6,601,653

Mined by

⛏️ P2SHAGD4ELPmV9VxECkLLRQiFxvMNQsYtybN6f

Merkle Root

fbf5ad26ccc317f2e194173aafc3369f463006af94987946532a1d4c117dfb33
Transactions (1)
Coinbasefbf5ad26ccc317…2a1d4c117dfb33
1 in β†’ 1 out10.1800 XPM109 B
AGD4ELPm…sYtybN6f
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.

7.963 Γ— 10⁸⁹(90-digit number)
79638774702839096980…50499830375059308339
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
7.963 Γ— 10⁸⁹(90-digit number)
79638774702839096980…50499830375059308339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.592 Γ— 10⁹⁰(91-digit number)
15927754940567819396…00999660750118616679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.185 Γ— 10⁹⁰(91-digit number)
31855509881135638792…01999321500237233359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.371 Γ— 10⁹⁰(91-digit number)
63711019762271277584…03998643000474466719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.274 Γ— 10⁹¹(92-digit number)
12742203952454255516…07997286000948933439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.548 Γ— 10⁹¹(92-digit number)
25484407904908511033…15994572001897866879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.096 Γ— 10⁹¹(92-digit number)
50968815809817022067…31989144003795733759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.019 Γ— 10⁹²(93-digit number)
10193763161963404413…63978288007591467519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.038 Γ— 10⁹²(93-digit number)
20387526323926808827…27956576015182935039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.077 Γ— 10⁹²(93-digit number)
40775052647853617654…55913152030365870079
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:57,715,100 XPMΒ·at block #6,808,880 Β· updates every 60s
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