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Block #3,373,848

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2019, 9:01:30 AM Β· Difficulty 10.9947 Β· 3,466,488 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9735f85a0516cff4f04901aeb279781a7f8fd289ba5f74a038efcb805107ccae
View on Chainz β†—

Height

#3,373,848

Difficulty

10.994713

Transactions

2

Size

425 B

Version

2

Bits

0afea589

Nonce

2,008,927,247

Timestamp

9/29/2019, 9:01:30 AM

Confirmations

3,466,488

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

c0fb85b4ae7573854e524109bd5720d178e0a1f19ff5d8d583168b4d8d1b6272
Transactions (2)
Coinbase08b86226409182…3c58a6626eeea2
1 in β†’ 1 out8.2700 XPM109 B
ASiq2qtK…VMhmk7yL
5045d2fa021a05…2b37a65f4cb98d
1 in β†’ 2 out170.8432 XPM226 B
APQ9gg1V…H4v8MyZ4AMLggddy…HpikgH98
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.

2.351 Γ— 10⁹⁡(96-digit number)
23515226420497815572…38970245980984842241
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
2.351 Γ— 10⁹⁡(96-digit number)
23515226420497815572…38970245980984842241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.703 Γ— 10⁹⁡(96-digit number)
47030452840995631144…77940491961969684481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.406 Γ— 10⁹⁡(96-digit number)
94060905681991262289…55880983923939368961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.881 Γ— 10⁹⁢(97-digit number)
18812181136398252457…11761967847878737921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.762 Γ— 10⁹⁢(97-digit number)
37624362272796504915…23523935695757475841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.524 Γ— 10⁹⁢(97-digit number)
75248724545593009831…47047871391514951681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.504 Γ— 10⁹⁷(98-digit number)
15049744909118601966…94095742783029903361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.009 Γ— 10⁹⁷(98-digit number)
30099489818237203932…88191485566059806721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.019 Γ— 10⁹⁷(98-digit number)
60198979636474407865…76382971132119613441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.203 Γ— 10⁹⁸(99-digit number)
12039795927294881573…52765942264239226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.407 Γ— 10⁹⁸(99-digit number)
24079591854589763146…05531884528478453761
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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