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Block #3,054,183

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/15/2019, 4:59:49 PM Β· Difficulty 11.0029 Β· 3,787,322 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66526c1c1ee6a3cc791a809ecd8e10d584fde7afeb1b5fce3fb271fa6aae88c1
View on Chainz β†—

Height

#3,054,183

Difficulty

11.002926

Transactions

1

Size

200 B

Version

2

Bits

0b00bfbf

Nonce

422,139,253

Timestamp

2/15/2019, 4:59:49 PM

Confirmations

3,787,322

Mined by

⛏️ P2SHAUhjokokGBrQRx2CtHWNPSvbj6k5m93PZR

Merkle Root

047f87d28bcab7be90f839f1d9961228764737e7980dac507faafdbc1fac2489
Transactions (1)
Coinbase047f87d28bcab7…aafdbc1fac2489
1 in β†’ 1 out8.2500 XPM110 B
AUhjokok…k5m93PZR
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.

9.283 Γ— 10⁹³(94-digit number)
92830886109281381757…13058042600608270241
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
9.283 Γ— 10⁹³(94-digit number)
92830886109281381757…13058042600608270241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.856 Γ— 10⁹⁴(95-digit number)
18566177221856276351…26116085201216540481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.713 Γ— 10⁹⁴(95-digit number)
37132354443712552702…52232170402433080961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.426 Γ— 10⁹⁴(95-digit number)
74264708887425105405…04464340804866161921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.485 Γ— 10⁹⁡(96-digit number)
14852941777485021081…08928681609732323841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.970 Γ— 10⁹⁡(96-digit number)
29705883554970042162…17857363219464647681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.941 Γ— 10⁹⁡(96-digit number)
59411767109940084324…35714726438929295361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.188 Γ— 10⁹⁢(97-digit number)
11882353421988016864…71429452877858590721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.376 Γ— 10⁹⁢(97-digit number)
23764706843976033729…42858905755717181441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.752 Γ— 10⁹⁢(97-digit number)
47529413687952067459…85717811511434362881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
9.505 Γ— 10⁹⁢(97-digit number)
95058827375904134919…71435623022868725761
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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