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Block #2,112,829

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/12/2017, 1:16:27 PM Β· Difficulty 10.8997 Β· 4,729,229 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
47afb22e0ec20f7e55591f277e9480124e5f555b047e6395936a1a5be96a78fb
View on Chainz β†—

Height

#2,112,829

Difficulty

10.899702

Transactions

2

Size

1.11 KB

Version

2

Bits

0ae652e1

Nonce

76,331,640

Timestamp

5/12/2017, 1:16:27 PM

Confirmations

4,729,229

Mined by

⛏️ P2SHAW1M7qLQDmjQv6zJFD9gmz5H7YXrQ5BpkD

Merkle Root

f7aaedbe50156101bd7e6f42af4ff12201d75c3bde6a188f081a5dcf42922a39
Transactions (2)
Coinbase8777870c7747cb…d79bb6f37ca51e
1 in β†’ 1 out8.4100 XPM109 B
AW1M7qLQ…XrQ5BpkD
ecfda0e6ae98dd…d6248e6349919b
6 in β†’ 1 out905.2213 XPM932 B
AQZVhvkQ…55MyFfM2
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.

2.709 Γ— 10⁹⁢(97-digit number)
27090412157703637775…48802669500612961281
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
2.709 Γ— 10⁹⁢(97-digit number)
27090412157703637775…48802669500612961281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.418 Γ— 10⁹⁢(97-digit number)
54180824315407275550…97605339001225922561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.083 Γ— 10⁹⁷(98-digit number)
10836164863081455110…95210678002451845121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.167 Γ— 10⁹⁷(98-digit number)
21672329726162910220…90421356004903690241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.334 Γ— 10⁹⁷(98-digit number)
43344659452325820440…80842712009807380481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.668 Γ— 10⁹⁷(98-digit number)
86689318904651640880…61685424019614760961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.733 Γ— 10⁹⁸(99-digit number)
17337863780930328176…23370848039229521921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.467 Γ— 10⁹⁸(99-digit number)
34675727561860656352…46741696078459043841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.935 Γ— 10⁹⁸(99-digit number)
69351455123721312704…93483392156918087681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.387 Γ— 10⁹⁹(100-digit number)
13870291024744262540…86966784313836175361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.774 Γ— 10⁹⁹(100-digit number)
27740582049488525081…73933568627672350721
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:57,980,846 XPMΒ·at block #6,842,057 Β· updates every 60s
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