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Block #3,248,725

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/1/2019, 8:23:06 AM Β· Difficulty 11.0065 Β· 3,594,199 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0dd03d32da478527c0c57ca164cfe499f22d67bfeef528312fa8f70dadfa8f7a
View on Chainz β†—

Height

#3,248,725

Difficulty

11.006460

Transactions

2

Size

1.46 KB

Version

2

Bits

0b01a761

Nonce

102,604,930

Timestamp

7/1/2019, 8:23:06 AM

Confirmations

3,594,199

Mined by

⛏️ P2SHARbm48qRsZyALB7gqdgsMMKGGA9xQc8DBX

Merkle Root

5676e949f34513752c4d6b1e3268541a439bda7fd812950860a1c546e6589056
Transactions (2)
Coinbase58d80506470b60…69e3492271772d
1 in β†’ 1 out8.2600 XPM110 B
ARbm48qR…9xQc8DBX
3a05892870084e…8f6e14f4fb9e43
7 in β†’ 1 out79.4804 XPM1.27 KB
AP6Q4fn7…DEPLFCuq
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.

8.354 Γ— 10⁹⁡(96-digit number)
83548735290821746349…55312124472606720001
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
8.354 Γ— 10⁹⁡(96-digit number)
83548735290821746349…55312124472606720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.670 Γ— 10⁹⁢(97-digit number)
16709747058164349269…10624248945213440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.341 Γ— 10⁹⁢(97-digit number)
33419494116328698539…21248497890426880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.683 Γ— 10⁹⁢(97-digit number)
66838988232657397079…42496995780853760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.336 Γ— 10⁹⁷(98-digit number)
13367797646531479415…84993991561707520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.673 Γ— 10⁹⁷(98-digit number)
26735595293062958831…69987983123415040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.347 Γ— 10⁹⁷(98-digit number)
53471190586125917663…39975966246830080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.069 Γ— 10⁹⁸(99-digit number)
10694238117225183532…79951932493660160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.138 Γ— 10⁹⁸(99-digit number)
21388476234450367065…59903864987320320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.277 Γ— 10⁹⁸(99-digit number)
42776952468900734131…19807729974640640001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.555 Γ— 10⁹⁸(99-digit number)
85553904937801468262…39615459949281280001
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:57,987,740 XPMΒ·at block #6,842,923 Β· updates every 60s
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