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Block #2,812,994

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/28/2018, 12:19:46 AM Β· Difficulty 11.6750 Β· 4,020,687 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8440c3742d6a24fa7d0872de50f33923eace4e0e56fa8866b590e57acfa00114
View on Chainz β†—

Height

#2,812,994

Difficulty

11.675037

Transactions

2

Size

872 B

Version

2

Bits

0baccf38

Nonce

1,778,781,555

Timestamp

8/28/2018, 12:19:46 AM

Confirmations

4,020,687

Mined by

⛏️ P2SHAQMW7X9YQMwHvYYM44TchEu8WK95ZUdVSA

Merkle Root

e9906c36b5462ca56f51bf4f7cd50ac3f35792c946b7aa3529f81b7b3497545c
Transactions (2)
Coinbase52734bbca6288a…0b3f4d01f8d48b
1 in β†’ 1 out7.3300 XPM110 B
AQMW7X9Y…95ZUdVSA
27c1f36dfb10f5…ecdc6129e4b417
4 in β†’ 2 out552.0142 XPM672 B
AbKsgpKm…meMyn6QDAREE8vFg…mLm1S4Nw
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.

2.951 Γ— 10⁹⁴(95-digit number)
29516749940929627499…48312131939575824001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.951 Γ— 10⁹⁴(95-digit number)
29516749940929627499…48312131939575824001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.903 Γ— 10⁹⁴(95-digit number)
59033499881859254998…96624263879151648001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.180 Γ— 10⁹⁡(96-digit number)
11806699976371850999…93248527758303296001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.361 Γ— 10⁹⁡(96-digit number)
23613399952743701999…86497055516606592001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.722 Γ— 10⁹⁡(96-digit number)
47226799905487403998…72994111033213184001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.445 Γ— 10⁹⁡(96-digit number)
94453599810974807997…45988222066426368001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.889 Γ— 10⁹⁢(97-digit number)
18890719962194961599…91976444132852736001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.778 Γ— 10⁹⁢(97-digit number)
37781439924389923199…83952888265705472001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.556 Γ— 10⁹⁢(97-digit number)
75562879848779846398…67905776531410944001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.511 Γ— 10⁹⁷(98-digit number)
15112575969755969279…35811553062821888001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.022 Γ— 10⁹⁷(98-digit number)
30225151939511938559…71623106125643776001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,913,667 XPMΒ·at block #6,833,680 Β· updates every 60s
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