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Block #2,915,891

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/9/2018, 9:14:46 AM Β· Difficulty 11.4444 Β· 3,927,067 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4aafb2a11cf24bd6fd976a36ae0bec82bc5492e9205e70d0e195e90eaf72faea
View on Chainz β†—

Height

#2,915,891

Difficulty

11.444398

Transactions

1

Size

201 B

Version

2

Bits

0b71c40d

Nonce

180,376,471

Timestamp

11/9/2018, 9:14:46 AM

Confirmations

3,927,067

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

af10b9e20670f145f37175d655fd24a15ca6ca7099fe37cfee34891fe4a19c09
Transactions (1)
Coinbaseaf10b9e20670f1…34891fe4a19c09
1 in β†’ 1 out7.6200 XPM110 B
AbXwmGxD…4XXYP765
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.

2.244 Γ— 10⁹⁢(97-digit number)
22447450182300030455…33383743881662992641
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
2.244 Γ— 10⁹⁢(97-digit number)
22447450182300030455…33383743881662992641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.489 Γ— 10⁹⁢(97-digit number)
44894900364600060910…66767487763325985281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.978 Γ— 10⁹⁢(97-digit number)
89789800729200121821…33534975526651970561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.795 Γ— 10⁹⁷(98-digit number)
17957960145840024364…67069951053303941121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.591 Γ— 10⁹⁷(98-digit number)
35915920291680048728…34139902106607882241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.183 Γ— 10⁹⁷(98-digit number)
71831840583360097456…68279804213215764481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.436 Γ— 10⁹⁸(99-digit number)
14366368116672019491…36559608426431528961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.873 Γ— 10⁹⁸(99-digit number)
28732736233344038982…73119216852863057921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.746 Γ— 10⁹⁸(99-digit number)
57465472466688077965…46238433705726115841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.149 Γ— 10⁹⁹(100-digit number)
11493094493337615593…92476867411452231681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.298 Γ— 10⁹⁹(100-digit number)
22986188986675231186…84953734822904463361
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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