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Block #2,121,528

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 1:55:45 AM Β· Difficulty 10.9136 Β· 4,715,353 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1472f6d94325166cf929b9b27aa870baa1c35495de23eae747b6f17690a8f44a
View on Chainz β†—

Height

#2,121,528

Difficulty

10.913602

Transactions

1

Size

201 B

Version

2

Bits

0ae9e1ca

Nonce

425,780,959

Timestamp

5/18/2017, 1:55:45 AM

Confirmations

4,715,353

Mined by

⛏️ P2SHATysJ82CFgNR9GeKLXprpeqr8iiGDyedaR

Merkle Root

1ff35c288c202e2e709c06479f3858df60bffe5deae5195526201a6de7cf306b
Transactions (1)
Coinbase1ff35c288c202e…201a6de7cf306b
1 in β†’ 1 out8.3800 XPM110 B
ATysJ82C…iGDyedaR
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.

1.494 Γ— 10⁹⁢(97-digit number)
14942835106495003572…55291343266207252481
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
1.494 Γ— 10⁹⁢(97-digit number)
14942835106495003572…55291343266207252481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.988 Γ— 10⁹⁢(97-digit number)
29885670212990007145…10582686532414504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.977 Γ— 10⁹⁢(97-digit number)
59771340425980014290…21165373064829009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.195 Γ— 10⁹⁷(98-digit number)
11954268085196002858…42330746129658019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.390 Γ— 10⁹⁷(98-digit number)
23908536170392005716…84661492259316039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.781 Γ— 10⁹⁷(98-digit number)
47817072340784011432…69322984518632079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.563 Γ— 10⁹⁷(98-digit number)
95634144681568022864…38645969037264158721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.912 Γ— 10⁹⁸(99-digit number)
19126828936313604572…77291938074528317441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.825 Γ— 10⁹⁸(99-digit number)
38253657872627209145…54583876149056634881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.650 Γ— 10⁹⁸(99-digit number)
76507315745254418291…09167752298113269761
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,939,339 XPMΒ·at block #6,836,880 Β· updates every 60s
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