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Block #2,815,883

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/29/2018, 9:46:17 PM Β· Difficulty 11.6854 Β· 4,023,363 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c338d24b218120a7c2376d48d6ae862285747288a4c6a085121cf9dc4535af63
View on Chainz β†—

Height

#2,815,883

Difficulty

11.685443

Transactions

1

Size

200 B

Version

2

Bits

0baf7935

Nonce

1,371,894,547

Timestamp

8/29/2018, 9:46:17 PM

Confirmations

4,023,363

Mined by

⛏️ P2SHAbX5ApyTBucJFdqr2wZMf4t6jvsiNqTFq6

Merkle Root

5450fab0cad520f7d938427bdb5fa1f5cc45ba6e8b887cfa12750ccc0fb99814
Transactions (1)
Coinbase5450fab0cad520…750ccc0fb99814
1 in β†’ 1 out7.3100 XPM110 B
AbX5ApyT…siNqTFq6
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.

1.193 Γ— 10⁹⁡(96-digit number)
11937298003067924690…81885065566765140481
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
1.193 Γ— 10⁹⁡(96-digit number)
11937298003067924690…81885065566765140481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.387 Γ— 10⁹⁡(96-digit number)
23874596006135849381…63770131133530280961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.774 Γ— 10⁹⁡(96-digit number)
47749192012271698763…27540262267060561921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.549 Γ— 10⁹⁡(96-digit number)
95498384024543397527…55080524534121123841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.909 Γ— 10⁹⁢(97-digit number)
19099676804908679505…10161049068242247681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.819 Γ— 10⁹⁢(97-digit number)
38199353609817359011…20322098136484495361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.639 Γ— 10⁹⁢(97-digit number)
76398707219634718022…40644196272968990721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.527 Γ— 10⁹⁷(98-digit number)
15279741443926943604…81288392545937981441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.055 Γ— 10⁹⁷(98-digit number)
30559482887853887208…62576785091875962881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.111 Γ— 10⁹⁷(98-digit number)
61118965775707774417…25153570183751925761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.222 Γ— 10⁹⁸(99-digit number)
12223793155141554883…50307140367503851521
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
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