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Block #2,634,930

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/29/2018, 1:53:28 AM Β· Difficulty 11.2800 Β· 4,207,100 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7539916e0b06609169f2a6a0e4cbee7380e05abd4b9744007e34f637e6fbd9c
View on Chainz β†—

Height

#2,634,930

Difficulty

11.279969

Transactions

1

Size

201 B

Version

2

Bits

0b47ac13

Nonce

245,343,846

Timestamp

4/29/2018, 1:53:28 AM

Confirmations

4,207,100

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

5b86214df233f301c16832b302552b11bc75407c890278da3ad23f451af93dcf
Transactions (1)
Coinbase5b86214df233f3…d23f451af93dcf
1 in β†’ 1 out7.8500 XPM110 B
Adqah8zh…1WwoHJ9t
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.

1.965 Γ— 10⁹⁢(97-digit number)
19659595454866466172…19045966142068527361
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
1.965 Γ— 10⁹⁢(97-digit number)
19659595454866466172…19045966142068527361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.931 Γ— 10⁹⁢(97-digit number)
39319190909732932344…38091932284137054721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.863 Γ— 10⁹⁢(97-digit number)
78638381819465864688…76183864568274109441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.572 Γ— 10⁹⁷(98-digit number)
15727676363893172937…52367729136548218881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.145 Γ— 10⁹⁷(98-digit number)
31455352727786345875…04735458273096437761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.291 Γ— 10⁹⁷(98-digit number)
62910705455572691750…09470916546192875521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.258 Γ— 10⁹⁸(99-digit number)
12582141091114538350…18941833092385751041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.516 Γ— 10⁹⁸(99-digit number)
25164282182229076700…37883666184771502081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.032 Γ— 10⁹⁸(99-digit number)
50328564364458153400…75767332369543004161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.006 Γ— 10⁹⁹(100-digit number)
10065712872891630680…51534664739086008321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.013 Γ— 10⁹⁹(100-digit number)
20131425745783261360…03069329478172016641
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
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