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Block #2,828,789

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/7/2018, 1:33:27 PM Β· Difficulty 11.7122 Β· 4,011,623 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3e9c154ab1179ddfa17667cd339bc36ff86154a984b9ddd9e0db47f4ed841251
View on Chainz β†—

Height

#2,828,789

Difficulty

11.712187

Transactions

1

Size

200 B

Version

2

Bits

0bb651e6

Nonce

1,761,790,884

Timestamp

9/7/2018, 1:33:27 PM

Confirmations

4,011,623

Mined by

⛏️ P2SHAN7dGa2RXvr8WJHYPhxHQ5bgBB5qtwchAM

Merkle Root

cc33fd86609519141f5767b0da6dd6bbde17c801d913f727cb2425aa8b888799
Transactions (1)
Coinbasecc33fd86609519…2425aa8b888799
1 in β†’ 1 out7.2800 XPM110 B
AN7dGa2R…5qtwchAM
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.

2.140 Γ— 10⁹⁴(95-digit number)
21407352759314969902…27017572509903618561
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
2.140 Γ— 10⁹⁴(95-digit number)
21407352759314969902…27017572509903618561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.281 Γ— 10⁹⁴(95-digit number)
42814705518629939805…54035145019807237121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.562 Γ— 10⁹⁴(95-digit number)
85629411037259879610…08070290039614474241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.712 Γ— 10⁹⁡(96-digit number)
17125882207451975922…16140580079228948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.425 Γ— 10⁹⁡(96-digit number)
34251764414903951844…32281160158457896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.850 Γ— 10⁹⁡(96-digit number)
68503528829807903688…64562320316915793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.370 Γ— 10⁹⁢(97-digit number)
13700705765961580737…29124640633831587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.740 Γ— 10⁹⁢(97-digit number)
27401411531923161475…58249281267663175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.480 Γ— 10⁹⁢(97-digit number)
54802823063846322950…16498562535326351361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.096 Γ— 10⁹⁷(98-digit number)
10960564612769264590…32997125070652702721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.192 Γ— 10⁹⁷(98-digit number)
21921129225538529180…65994250141305405441
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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