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Block #2,649,478

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/5/2018, 6:53:51 AM Β· Difficulty 11.7637 Β· 4,183,508 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d44eb3bb64ad5b4b3f3cf74ee1ed7ec365dd2da22befdcb937c850308a929208
View on Chainz β†—

Height

#2,649,478

Difficulty

11.763714

Transactions

1

Size

200 B

Version

2

Bits

0bc382cb

Nonce

391,895,047

Timestamp

5/5/2018, 6:53:51 AM

Confirmations

4,183,508

Mined by

⛏️ P2SHALt6GpYondMCm13BeMCVrMmp9baZtj2Uxa

Merkle Root

6f508cbb2316790dacaedd214391cb6a1140ee1ff7e6d21b04c85619523e640d
Transactions (1)
Coinbase6f508cbb231679…c85619523e640d
1 in β†’ 1 out7.2100 XPM110 B
ALt6GpYo…aZtj2Uxa
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.

8.115 Γ— 10⁹⁡(96-digit number)
81156455352662267879…10224557768040396801
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
8.115 Γ— 10⁹⁡(96-digit number)
81156455352662267879…10224557768040396801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.623 Γ— 10⁹⁢(97-digit number)
16231291070532453575…20449115536080793601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.246 Γ— 10⁹⁢(97-digit number)
32462582141064907151…40898231072161587201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.492 Γ— 10⁹⁢(97-digit number)
64925164282129814303…81796462144323174401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.298 Γ— 10⁹⁷(98-digit number)
12985032856425962860…63592924288646348801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.597 Γ— 10⁹⁷(98-digit number)
25970065712851925721…27185848577292697601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.194 Γ— 10⁹⁷(98-digit number)
51940131425703851442…54371697154585395201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.038 Γ— 10⁹⁸(99-digit number)
10388026285140770288…08743394309170790401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.077 Γ— 10⁹⁸(99-digit number)
20776052570281540577…17486788618341580801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.155 Γ— 10⁹⁸(99-digit number)
41552105140563081154…34973577236683161601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
8.310 Γ— 10⁹⁸(99-digit number)
83104210281126162308…69947154473366323201
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:57,908,058 XPMΒ·at block #6,832,985 Β· updates every 60s
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