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Block #2,831,646

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/9/2018, 11:36:31 AM Β· Difficulty 11.7175 Β· 4,006,385 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7738c76c1822d922e9cc49c00cde8a5cb4da59b671da3954478fb619b3a55c11
View on Chainz β†—

Height

#2,831,646

Difficulty

11.717506

Transactions

1

Size

200 B

Version

2

Bits

0bb7ae72

Nonce

1,343,882,081

Timestamp

9/9/2018, 11:36:31 AM

Confirmations

4,006,385

Mined by

⛏️ P2SHAaq8YX7AvoxamG5o3ghnf65BDZTuEkQxrQ

Merkle Root

ee1e57a40d403dd567a901ebd2b8d1e778fa77a18a86595219b96eaee09de578
Transactions (1)
Coinbaseee1e57a40d403d…b96eaee09de578
1 in β†’ 1 out7.2700 XPM110 B
Aaq8YX7A…TuEkQxrQ
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.

6.777 Γ— 10⁹³(94-digit number)
67770682855520580907…31691847421376321959
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
6.777 Γ— 10⁹³(94-digit number)
67770682855520580907…31691847421376321959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.355 Γ— 10⁹⁴(95-digit number)
13554136571104116181…63383694842752643919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.710 Γ— 10⁹⁴(95-digit number)
27108273142208232362…26767389685505287839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.421 Γ— 10⁹⁴(95-digit number)
54216546284416464725…53534779371010575679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.084 Γ— 10⁹⁡(96-digit number)
10843309256883292945…07069558742021151359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.168 Γ— 10⁹⁡(96-digit number)
21686618513766585890…14139117484042302719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.337 Γ— 10⁹⁡(96-digit number)
43373237027533171780…28278234968084605439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.674 Γ— 10⁹⁡(96-digit number)
86746474055066343561…56556469936169210879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.734 Γ— 10⁹⁢(97-digit number)
17349294811013268712…13112939872338421759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.469 Γ— 10⁹⁢(97-digit number)
34698589622026537424…26225879744676843519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.939 Γ— 10⁹⁢(97-digit number)
69397179244053074849…52451759489353687039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,948,598 XPMΒ·at block #6,838,030 Β· updates every 60s
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