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Block #2,826,923

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/6/2018, 7:00:06 AM Β· Difficulty 11.7102 Β· 4,013,160 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f9635c3131f7935b72431fb764aa3e2a159c0c56bef9f41f683224e509ed0744
View on Chainz β†—

Height

#2,826,923

Difficulty

11.710162

Transactions

1

Size

200 B

Version

2

Bits

0bb5cd2a

Nonce

55,461,749

Timestamp

9/6/2018, 7:00:06 AM

Confirmations

4,013,160

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

a046d62f6d4f018930ca52a4af1d93b6cd8d871a7b317c4c6a9613f5cf0a65cb
Transactions (1)
Coinbasea046d62f6d4f01…9613f5cf0a65cb
1 in β†’ 1 out7.2800 XPM110 B
AZtxQr2F…7grUWrUz
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.

2.127 Γ— 10⁹⁴(95-digit number)
21274382145790712360…91712438492799111681
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
2.127 Γ— 10⁹⁴(95-digit number)
21274382145790712360…91712438492799111681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.254 Γ— 10⁹⁴(95-digit number)
42548764291581424721…83424876985598223361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.509 Γ— 10⁹⁴(95-digit number)
85097528583162849443…66849753971196446721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.701 Γ— 10⁹⁡(96-digit number)
17019505716632569888…33699507942392893441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.403 Γ— 10⁹⁡(96-digit number)
34039011433265139777…67399015884785786881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.807 Γ— 10⁹⁡(96-digit number)
68078022866530279554…34798031769571573761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.361 Γ— 10⁹⁢(97-digit number)
13615604573306055910…69596063539143147521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.723 Γ— 10⁹⁢(97-digit number)
27231209146612111821…39192127078286295041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.446 Γ— 10⁹⁢(97-digit number)
54462418293224223643…78384254156572590081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.089 Γ— 10⁹⁷(98-digit number)
10892483658644844728…56768508313145180161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.178 Γ— 10⁹⁷(98-digit number)
21784967317289689457…13537016626290360321
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
Circulating Supply:57,964,972 XPMΒ·at block #6,840,082 Β· updates every 60s
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