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Block #2,040,072

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/27/2017, 12:17:41 AM Β· Difficulty 10.6794 Β· 4,776,729 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cebb772c28e7fc00c7a5c280baaf208b0e10e039cd9b70fa65281f5a1e4be3d8
View on Chainz β†—

Height

#2,040,072

Difficulty

10.679448

Transactions

2

Size

425 B

Version

2

Bits

0aadf048

Nonce

1,535,425,345

Timestamp

3/27/2017, 12:17:41 AM

Confirmations

4,776,729

Mined by

⛏️ P2SHARniRdhuCaWPCXRuftCZdpBvmtomZnUkni

Merkle Root

de9c1ded238960aeea5e2eb20c507db091ad127f7679582f8032ad91c7d2b02b
Transactions (2)
Coinbase14001103538b45…7d2bb441467967
1 in β†’ 1 out8.7600 XPM109 B
ARniRdhu…omZnUkni
3214f0a035e90e…a52f694252ee01
1 in β†’ 2 out79099.9800 XPM226 B
AVPaHs9p…2qBBuetxAVPU2i57…kYsH8BA4
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.

1.156 Γ— 10⁹⁴(95-digit number)
11565865352898919813…81475877552830086551
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
1.156 Γ— 10⁹⁴(95-digit number)
11565865352898919813…81475877552830086551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.313 Γ— 10⁹⁴(95-digit number)
23131730705797839627…62951755105660173101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.626 Γ— 10⁹⁴(95-digit number)
46263461411595679254…25903510211320346201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.252 Γ— 10⁹⁴(95-digit number)
92526922823191358508…51807020422640692401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.850 Γ— 10⁹⁡(96-digit number)
18505384564638271701…03614040845281384801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.701 Γ— 10⁹⁡(96-digit number)
37010769129276543403…07228081690562769601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.402 Γ— 10⁹⁡(96-digit number)
74021538258553086806…14456163381125539201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.480 Γ— 10⁹⁢(97-digit number)
14804307651710617361…28912326762251078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.960 Γ— 10⁹⁢(97-digit number)
29608615303421234722…57824653524502156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.921 Γ— 10⁹⁢(97-digit number)
59217230606842469445…15649307049004313601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,778,444 XPMΒ·at block #6,816,800 Β· updates every 60s
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