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Block #2,645,499

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/2/2018, 10:41:57 PM Β· Difficulty 11.7333 Β· 4,197,490 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7382d2d350d8b818c3d973774a1e1f51f210e2c9685ce2ebdfdc8ce073735724
View on Chainz β†—

Height

#2,645,499

Difficulty

11.733309

Transactions

1

Size

200 B

Version

2

Bits

0bbbba21

Nonce

663,205,797

Timestamp

5/2/2018, 10:41:57 PM

Confirmations

4,197,490

Mined by

⛏️ P2SHAaeQwr8t4xy7GfDPuYALNJjr2CdrFSM3hL

Merkle Root

b40c4ed255710f22722fe3f97e6304f0ea85db4d96510c7f9005e5f5f95be948
Transactions (1)
Coinbaseb40c4ed255710f…05e5f5f95be948
1 in β†’ 1 out7.2500 XPM110 B
AaeQwr8t…drFSM3hL
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.

3.332 Γ— 10⁹³(94-digit number)
33323913479634098626…36684295432524527201
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
3.332 Γ— 10⁹³(94-digit number)
33323913479634098626…36684295432524527201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.664 Γ— 10⁹³(94-digit number)
66647826959268197253…73368590865049054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.332 Γ— 10⁹⁴(95-digit number)
13329565391853639450…46737181730098108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.665 Γ— 10⁹⁴(95-digit number)
26659130783707278901…93474363460196217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.331 Γ— 10⁹⁴(95-digit number)
53318261567414557803…86948726920392435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.066 Γ— 10⁹⁡(96-digit number)
10663652313482911560…73897453840784870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.132 Γ— 10⁹⁡(96-digit number)
21327304626965823121…47794907681569740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.265 Γ— 10⁹⁡(96-digit number)
42654609253931646242…95589815363139481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.530 Γ— 10⁹⁡(96-digit number)
85309218507863292485…91179630726278963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.706 Γ— 10⁹⁢(97-digit number)
17061843701572658497…82359261452557926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.412 Γ— 10⁹⁢(97-digit number)
34123687403145316994…64718522905115852801
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:57,988,268 XPMΒ·at block #6,842,988 Β· updates every 60s
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