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Block #1,801,828

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/11/2016, 5:56:15 AM Β· Difficulty 10.7715 Β· 5,025,298 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f4fa4df6700f5d0269a4ee6d97d3377fa75bc1e49cb941cfe94c7671a9b54010
View on Chainz β†—

Height

#1,801,828

Difficulty

10.771486

Transactions

1

Size

242 B

Version

2

Bits

0ac5801c

Nonce

234,464,524

Timestamp

10/11/2016, 5:56:15 AM

Confirmations

5,025,298

Mined by

⛏️ P2SHATd5Bq5SNppozp9HDzLQKxc4KVPcfPgHVj

Merkle Root

c7696fec6110fa794180ee5ff0a22977bcda9a973cea531fae15e29da767b91a
Transactions (1)
Coinbasec7696fec6110fa…15e29da767b91a
1 in β†’ 2 out8.6100 XPM152 B
ATd5Bq5S…PcfPgHVjALPu3s2c…EJXLjVFh
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.

2.032 Γ— 10⁹⁡(96-digit number)
20329131880100136262…83920379711533176401
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
2.032 Γ— 10⁹⁡(96-digit number)
20329131880100136262…83920379711533176401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.065 Γ— 10⁹⁡(96-digit number)
40658263760200272524…67840759423066352801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.131 Γ— 10⁹⁡(96-digit number)
81316527520400545049…35681518846132705601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.626 Γ— 10⁹⁢(97-digit number)
16263305504080109009…71363037692265411201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.252 Γ— 10⁹⁢(97-digit number)
32526611008160218019…42726075384530822401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.505 Γ— 10⁹⁢(97-digit number)
65053222016320436039…85452150769061644801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.301 Γ— 10⁹⁷(98-digit number)
13010644403264087207…70904301538123289601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.602 Γ— 10⁹⁷(98-digit number)
26021288806528174415…41808603076246579201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.204 Γ— 10⁹⁷(98-digit number)
52042577613056348831…83617206152493158401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.040 Γ— 10⁹⁸(99-digit number)
10408515522611269766…67234412304986316801
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:57,861,190 XPMΒ·at block #6,827,125 Β· updates every 60s
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