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Block #3,095,989

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/16/2019, 4:35:27 PM Β· Difficulty 11.0826 Β· 3,746,908 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7dc88b4ad1b0083acd9fbb88df5b7c5478ff6f5f138e01d95554ca6ec9bb30a
View on Chainz β†—

Height

#3,095,989

Difficulty

11.082611

Transactions

1

Size

201 B

Version

2

Bits

0b1525fa

Nonce

10,508,939

Timestamp

3/16/2019, 4:35:27 PM

Confirmations

3,746,908

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

b96e0ca582daf406f70bf3e128b684e36d592aa850a28e62b23ae18c998c9a44
Transactions (1)
Coinbaseb96e0ca582daf4…3ae18c998c9a44
1 in β†’ 1 out8.1300 XPM110 B
AbXwmGxD…4XXYP765
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.

3.262 Γ— 10⁹⁷(98-digit number)
32627167464924062476…09063824517350318081
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
3.262 Γ— 10⁹⁷(98-digit number)
32627167464924062476…09063824517350318081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.525 Γ— 10⁹⁷(98-digit number)
65254334929848124953…18127649034700636161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.305 Γ— 10⁹⁸(99-digit number)
13050866985969624990…36255298069401272321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.610 Γ— 10⁹⁸(99-digit number)
26101733971939249981…72510596138802544641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.220 Γ— 10⁹⁸(99-digit number)
52203467943878499962…45021192277605089281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.044 Γ— 10⁹⁹(100-digit number)
10440693588775699992…90042384555210178561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.088 Γ— 10⁹⁹(100-digit number)
20881387177551399984…80084769110420357121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.176 Γ— 10⁹⁹(100-digit number)
41762774355102799969…60169538220840714241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
8.352 Γ— 10⁹⁹(100-digit number)
83525548710205599939…20339076441681428481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.670 Γ— 10¹⁰⁰(101-digit number)
16705109742041119987…40678152883362856961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.341 Γ— 10¹⁰⁰(101-digit number)
33410219484082239975…81356305766725713921
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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