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Block #2,020,663

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/13/2017, 2:57:33 AM Β· Difficulty 10.7145 Β· 4,811,153 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
002cd2973b2ebf5e66e8f6e95184fc35e5547b7b7f3d454fc1bf978581949a06
View on Chainz β†—

Height

#2,020,663

Difficulty

10.714457

Transactions

1

Size

199 B

Version

2

Bits

0ab6e6a2

Nonce

1,250,306,527

Timestamp

3/13/2017, 2:57:33 AM

Confirmations

4,811,153

Mined by

⛏️ P2SHAM2BTpyXMLpMVa4HqtZB1zMoZkcjimfX3U

Merkle Root

5e232f406e90e140bad8b13db4daa779d96531bce5f2fe97dc9e362365e74545
Transactions (1)
Coinbase5e232f406e90e1…9e362365e74545
1 in β†’ 1 out8.7000 XPM109 B
AM2BTpyX…cjimfX3U
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.

5.315 Γ— 10⁹⁴(95-digit number)
53153463122189070772…26571285803514093761
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
5.315 Γ— 10⁹⁴(95-digit number)
53153463122189070772…26571285803514093761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.063 Γ— 10⁹⁡(96-digit number)
10630692624437814154…53142571607028187521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.126 Γ— 10⁹⁡(96-digit number)
21261385248875628309…06285143214056375041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.252 Γ— 10⁹⁡(96-digit number)
42522770497751256618…12570286428112750081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.504 Γ— 10⁹⁡(96-digit number)
85045540995502513236…25140572856225500161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.700 Γ— 10⁹⁢(97-digit number)
17009108199100502647…50281145712451000321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.401 Γ— 10⁹⁢(97-digit number)
34018216398201005294…00562291424902000641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.803 Γ— 10⁹⁢(97-digit number)
68036432796402010589…01124582849804001281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.360 Γ— 10⁹⁷(98-digit number)
13607286559280402117…02249165699608002561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.721 Γ— 10⁹⁷(98-digit number)
27214573118560804235…04498331399216005121
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:57,898,644 XPMΒ·at block #6,831,815 Β· updates every 60s
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