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Block #2,005,200

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/2/2017, 6:56:57 AM Β· Difficulty 10.7214 Β· 4,837,503 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
256e9b50703790e351d24dab4b673fe9724651b29624e63a45a9ac27f5b7b50c
View on Chainz β†—

Height

#2,005,200

Difficulty

10.721358

Transactions

1

Size

201 B

Version

2

Bits

0ab8aae9

Nonce

1,115,985,241

Timestamp

3/2/2017, 6:56:57 AM

Confirmations

4,837,503

Mined by

⛏️ P2SHAG7XSgR4UGkpxN122hTtGrnUBDJYpzEsM5

Merkle Root

1001b39fea645119452d003e972ad2bfa52e38eec8eaf04013caa790fdb0489e
Transactions (1)
Coinbase1001b39fea6451…caa790fdb0489e
1 in β†’ 1 out8.6900 XPM110 B
AG7XSgR4…JYpzEsM5
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.

1.438 Γ— 10⁹⁷(98-digit number)
14387931528406626600…98659522702703226881
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
1.438 Γ— 10⁹⁷(98-digit number)
14387931528406626600…98659522702703226881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.877 Γ— 10⁹⁷(98-digit number)
28775863056813253201…97319045405406453761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.755 Γ— 10⁹⁷(98-digit number)
57551726113626506402…94638090810812907521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.151 Γ— 10⁹⁸(99-digit number)
11510345222725301280…89276181621625815041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.302 Γ— 10⁹⁸(99-digit number)
23020690445450602560…78552363243251630081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.604 Γ— 10⁹⁸(99-digit number)
46041380890901205121…57104726486503260161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.208 Γ— 10⁹⁸(99-digit number)
92082761781802410243…14209452973006520321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.841 Γ— 10⁹⁹(100-digit number)
18416552356360482048…28418905946013040641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.683 Γ— 10⁹⁹(100-digit number)
36833104712720964097…56837811892026081281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.366 Γ— 10⁹⁹(100-digit number)
73666209425441928195…13675623784052162561
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:57,985,973 XPMΒ·at block #6,842,702 Β· updates every 60s
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