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Block #3,082,559

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/7/2019, 2:15:34 PM Β· Difficulty 11.0199 Β· 3,759,590 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
91ece551ad1e68809e6958255fad7fb07ec22ff75e9ba521296fc256e53864fe
View on Chainz β†—

Height

#3,082,559

Difficulty

11.019892

Transactions

1

Size

199 B

Version

2

Bits

0b0517a8

Nonce

798,816,658

Timestamp

3/7/2019, 2:15:34 PM

Confirmations

3,759,590

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

b525edd82c004aa6a83f099152630dad609d1808ebbe0efe0de84342d7e05d72
Transactions (1)
Coinbaseb525edd82c004a…e84342d7e05d72
1 in β†’ 1 out8.2200 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.

3.663 Γ— 10⁹²(93-digit number)
36630761641902890867…50908681295043437601
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
3.663 Γ— 10⁹²(93-digit number)
36630761641902890867…50908681295043437601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.326 Γ— 10⁹²(93-digit number)
73261523283805781735…01817362590086875201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.465 Γ— 10⁹³(94-digit number)
14652304656761156347…03634725180173750401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.930 Γ— 10⁹³(94-digit number)
29304609313522312694…07269450360347500801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.860 Γ— 10⁹³(94-digit number)
58609218627044625388…14538900720695001601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.172 Γ— 10⁹⁴(95-digit number)
11721843725408925077…29077801441390003201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.344 Γ— 10⁹⁴(95-digit number)
23443687450817850155…58155602882780006401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.688 Γ— 10⁹⁴(95-digit number)
46887374901635700310…16311205765560012801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.377 Γ— 10⁹⁴(95-digit number)
93774749803271400621…32622411531120025601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.875 Γ— 10⁹⁡(96-digit number)
18754949960654280124…65244823062240051201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.750 Γ— 10⁹⁡(96-digit number)
37509899921308560248…30489646124480102401
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:57,981,581 XPMΒ·at block #6,842,148 Β· updates every 60s
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