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Block #1,412,139

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/13/2016, 9:57:03 PM Β· Difficulty 10.8040 Β· 5,427,138 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d82531b15eee64a550037749c66cb2cd7f90bb293dfca774c83ec332b1091370
View on Chainz β†—

Height

#1,412,139

Difficulty

10.804005

Transactions

1

Size

200 B

Version

2

Bits

0acdd344

Nonce

37,310,205

Timestamp

1/13/2016, 9:57:03 PM

Confirmations

5,427,138

Mined by

⛏️ P2SHAQZAi9oFgmTQJKqKDtwyVpC3H99Z4ftGqd

Merkle Root

8fbcef25b388e061904fa235482f5c4dae9b07ed4979883de5f48bf53e65c1d8
Transactions (1)
Coinbase8fbcef25b388e0…f48bf53e65c1d8
1 in β†’ 1 out8.5500 XPM110 B
AQZAi9oF…9Z4ftGqd
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.

7.290 Γ— 10⁹³(94-digit number)
72906194502894938001…62350039517469840919
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
7.290 Γ— 10⁹³(94-digit number)
72906194502894938001…62350039517469840919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.458 Γ— 10⁹⁴(95-digit number)
14581238900578987600…24700079034939681839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.916 Γ— 10⁹⁴(95-digit number)
29162477801157975200…49400158069879363679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.832 Γ— 10⁹⁴(95-digit number)
58324955602315950401…98800316139758727359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁡(96-digit number)
11664991120463190080…97600632279517454719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.332 Γ— 10⁹⁡(96-digit number)
23329982240926380160…95201264559034909439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.665 Γ— 10⁹⁡(96-digit number)
46659964481852760321…90402529118069818879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.331 Γ— 10⁹⁡(96-digit number)
93319928963705520642…80805058236139637759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.866 Γ— 10⁹⁢(97-digit number)
18663985792741104128…61610116472279275519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.732 Γ— 10⁹⁢(97-digit number)
37327971585482208256…23220232944558551039
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:57,958,501 XPMΒ·at block #6,839,276 Β· updates every 60s
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