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Block #2,927,401

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/17/2018, 8:25:14 PM Β· Difficulty 11.3646 Β· 3,916,019 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bbd4d458dd08dbbec7bfa37ab086a200fe440b974784445e1e9d448bc6b1ba1a
View on Chainz β†—

Height

#2,927,401

Difficulty

11.364594

Transactions

1

Size

200 B

Version

2

Bits

0b5d560a

Nonce

1,962,474,685

Timestamp

11/17/2018, 8:25:14 PM

Confirmations

3,916,019

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

eb8eca567bfa9e2940897633ce2d3307d5c5a98ed8e481e35e638e3af3a45cfd
Transactions (1)
Coinbaseeb8eca567bfa9e…638e3af3a45cfd
1 in β†’ 1 out7.7300 XPM110 B
AUMQRepm…tAfKmdW1
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.

2.852 Γ— 10⁹⁴(95-digit number)
28520548698209011593…40430922366877874001
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
2.852 Γ— 10⁹⁴(95-digit number)
28520548698209011593…40430922366877874001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.704 Γ— 10⁹⁴(95-digit number)
57041097396418023187…80861844733755748001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.140 Γ— 10⁹⁡(96-digit number)
11408219479283604637…61723689467511496001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.281 Γ— 10⁹⁡(96-digit number)
22816438958567209274…23447378935022992001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.563 Γ— 10⁹⁡(96-digit number)
45632877917134418549…46894757870045984001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.126 Γ— 10⁹⁡(96-digit number)
91265755834268837099…93789515740091968001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.825 Γ— 10⁹⁢(97-digit number)
18253151166853767419…87579031480183936001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.650 Γ— 10⁹⁢(97-digit number)
36506302333707534839…75158062960367872001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.301 Γ— 10⁹⁢(97-digit number)
73012604667415069679…50316125920735744001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.460 Γ— 10⁹⁷(98-digit number)
14602520933483013935…00632251841471488001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.920 Γ— 10⁹⁷(98-digit number)
29205041866966027871…01264503682942976001
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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