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Block #2,811,501

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/27/2018, 1:25:12 AM Β· Difficulty 11.6672 Β· 4,028,310 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7462c1e235557ea67c2caa918246bd8f540926940150c4b2c5d399b356e0b1fa
View on Chainz β†—

Height

#2,811,501

Difficulty

11.667234

Transactions

1

Size

200 B

Version

2

Bits

0baacfdb

Nonce

460,476,308

Timestamp

8/27/2018, 1:25:12 AM

Confirmations

4,028,310

Mined by

⛏️ P2SHARiiAsK2ucRGE8Ev1xUFtZTfEobsrmfpti

Merkle Root

8a3a5fd48c6c8bf593dfa9390fcd7f5d071abb789c96b29d313fea94488937c2
Transactions (1)
Coinbase8a3a5fd48c6c8b…3fea94488937c2
1 in β†’ 1 out7.3300 XPM110 B
ARiiAsK2…bsrmfpti
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.

3.177 Γ— 10⁹⁡(96-digit number)
31772498463211044536…58215799797533274321
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
3.177 Γ— 10⁹⁡(96-digit number)
31772498463211044536…58215799797533274321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.354 Γ— 10⁹⁡(96-digit number)
63544996926422089073…16431599595066548641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.270 Γ— 10⁹⁢(97-digit number)
12708999385284417814…32863199190133097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.541 Γ— 10⁹⁢(97-digit number)
25417998770568835629…65726398380266194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.083 Γ— 10⁹⁢(97-digit number)
50835997541137671258…31452796760532389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.016 Γ— 10⁹⁷(98-digit number)
10167199508227534251…62905593521064778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.033 Γ— 10⁹⁷(98-digit number)
20334399016455068503…25811187042129556481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.066 Γ— 10⁹⁷(98-digit number)
40668798032910137006…51622374084259112961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.133 Γ— 10⁹⁷(98-digit number)
81337596065820274013…03244748168518225921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.626 Γ— 10⁹⁸(99-digit number)
16267519213164054802…06489496337036451841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.253 Γ— 10⁹⁸(99-digit number)
32535038426328109605…12978992674072903681
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:57,962,781 XPMΒ·at block #6,839,810 Β· updates every 60s
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