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Block #2,861,881

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/1/2018, 12:22:50 AM Β· Difficulty 11.6720 Β· 3,980,704 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
45240269626cbcc2aee78903280e072686f4f7389d48ae741662f7f0610de816
View on Chainz β†—

Height

#2,861,881

Difficulty

11.671994

Transactions

1

Size

200 B

Version

2

Bits

0bac07cb

Nonce

1,734,059,597

Timestamp

10/1/2018, 12:22:50 AM

Confirmations

3,980,704

Mined by

⛏️ P2SHAdHM1p1AC5DiwEoBqGxqzpHNCFa3RRF5V6

Merkle Root

164d3fc6d314c6953c3c05b0f40c14cf7b519ad9e73504b9f7fa201b3c8af0de
Transactions (1)
Coinbase164d3fc6d314c6…fa201b3c8af0de
1 in β†’ 1 out7.3300 XPM110 B
AdHM1p1A…a3RRF5V6
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.

6.490 Γ— 10⁹⁡(96-digit number)
64906073427882793482…39655662502124791041
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
6.490 Γ— 10⁹⁡(96-digit number)
64906073427882793482…39655662502124791041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.298 Γ— 10⁹⁢(97-digit number)
12981214685576558696…79311325004249582081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.596 Γ— 10⁹⁢(97-digit number)
25962429371153117392…58622650008499164161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.192 Γ— 10⁹⁢(97-digit number)
51924858742306234785…17245300016998328321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.038 Γ— 10⁹⁷(98-digit number)
10384971748461246957…34490600033996656641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.076 Γ— 10⁹⁷(98-digit number)
20769943496922493914…68981200067993313281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.153 Γ— 10⁹⁷(98-digit number)
41539886993844987828…37962400135986626561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.307 Γ— 10⁹⁷(98-digit number)
83079773987689975656…75924800271973253121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.661 Γ— 10⁹⁸(99-digit number)
16615954797537995131…51849600543946506241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.323 Γ— 10⁹⁸(99-digit number)
33231909595075990262…03699201087893012481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
6.646 Γ— 10⁹⁸(99-digit number)
66463819190151980525…07398402175786024961
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:57,985,109 XPMΒ·at block #6,842,584 Β· updates every 60s
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