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Block #2,630,632

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/26/2018, 1:36:20 PM Β· Difficulty 11.1758 Β· 4,211,079 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
71e51dd2c802ad285073597b94688949404a876d35cb61fca6c99c0201e01401
View on Chainz β†—

Height

#2,630,632

Difficulty

11.175821

Transactions

1

Size

200 B

Version

2

Bits

0b2d029f

Nonce

113,768,611

Timestamp

4/26/2018, 1:36:20 PM

Confirmations

4,211,079

Mined by

⛏️ P2SHAbHbyHnypbS6WXwWqMoiiUiQ4aZ7s89bYC

Merkle Root

c778cab6749dc0652f6a473d40b89eb0cbbeb1468d611561d541bb118f02135e
Transactions (1)
Coinbasec778cab6749dc0…41bb118f02135e
1 in β†’ 1 out7.9900 XPM110 B
AbHbyHny…Z7s89bYC
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.

3.413 Γ— 10⁹⁴(95-digit number)
34138802963555678276…17185695892856367681
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
3.413 Γ— 10⁹⁴(95-digit number)
34138802963555678276…17185695892856367681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.827 Γ— 10⁹⁴(95-digit number)
68277605927111356553…34371391785712735361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.365 Γ— 10⁹⁡(96-digit number)
13655521185422271310…68742783571425470721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.731 Γ— 10⁹⁡(96-digit number)
27311042370844542621…37485567142850941441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.462 Γ— 10⁹⁡(96-digit number)
54622084741689085242…74971134285701882881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.092 Γ— 10⁹⁢(97-digit number)
10924416948337817048…49942268571403765761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.184 Γ— 10⁹⁢(97-digit number)
21848833896675634097…99884537142807531521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.369 Γ— 10⁹⁢(97-digit number)
43697667793351268194…99769074285615063041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.739 Γ— 10⁹⁢(97-digit number)
87395335586702536388…99538148571230126081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.747 Γ— 10⁹⁷(98-digit number)
17479067117340507277…99076297142460252161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.495 Γ— 10⁹⁷(98-digit number)
34958134234681014555…98152594284920504321
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:57,978,067 XPMΒ·at block #6,841,710 Β· updates every 60s
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