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Block #3,457,258

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/1/2019, 7:44:22 PM Β· Difficulty 10.9788 Β· 3,385,861 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
13c3ab31c1dada67aaa2d28e3bf3d12ddea39caf821ac2f7236b498379469aea
View on Chainz β†—

Height

#3,457,258

Difficulty

10.978845

Transactions

2

Size

4.02 KB

Version

2

Bits

0afa9590

Nonce

10,614,944

Timestamp

12/1/2019, 7:44:22 PM

Confirmations

3,385,861

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

2f45d33c8525618c90d8b20874c921b0c3626a78178b5accfb139e6e9a7d9574
Transactions (2)
Coinbase934a8afe97b132…86b4969d830ebe
1 in β†’ 1 out8.3200 XPM110 B
ASiq2qtK…VMhmk7yL
e2ab907353173f…70c41428a4f5a4
26 in β†’ 2 out2860.4890 XPM3.83 KB
AX3W6pJy…NwZ88svUAdXePwZa…7CNTHBci
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.

2.163 Γ— 10⁹³(94-digit number)
21638283649422708925…39092775711249019921
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
2.163 Γ— 10⁹³(94-digit number)
21638283649422708925…39092775711249019921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.327 Γ— 10⁹³(94-digit number)
43276567298845417851…78185551422498039841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.655 Γ— 10⁹³(94-digit number)
86553134597690835702…56371102844996079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.731 Γ— 10⁹⁴(95-digit number)
17310626919538167140…12742205689992159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.462 Γ— 10⁹⁴(95-digit number)
34621253839076334280…25484411379984318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.924 Γ— 10⁹⁴(95-digit number)
69242507678152668561…50968822759968637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.384 Γ— 10⁹⁡(96-digit number)
13848501535630533712…01937645519937274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.769 Γ— 10⁹⁡(96-digit number)
27697003071261067424…03875291039874549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.539 Γ— 10⁹⁡(96-digit number)
55394006142522134849…07750582079749099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.107 Γ— 10⁹⁢(97-digit number)
11078801228504426969…15501164159498199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.215 Γ— 10⁹⁢(97-digit number)
22157602457008853939…31002328318996398081
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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