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Block #2,304,274

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/22/2017, 3:44:24 AM Β· Difficulty 10.9174 Β· 4,538,748 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bc6552ae6ef0eabe544fa354142ddc853f3f9441b61935ee18d13673bcaa8c2d
View on Chainz β†—

Height

#2,304,274

Difficulty

10.917441

Transactions

1

Size

199 B

Version

2

Bits

0aeadd6f

Nonce

527,019,098

Timestamp

9/22/2017, 3:44:24 AM

Confirmations

4,538,748

Mined by

⛏️ P2SHAMpTsUJtSTSC2uNcWZi1Gh71gh46xxKJFG

Merkle Root

70aadfc8c253597703a17d3fbc58701811efd8e4538bcccd2b206631c8f75d90
Transactions (1)
Coinbase70aadfc8c25359…206631c8f75d90
1 in β†’ 1 out8.3800 XPM109 B
AMpTsUJt…46xxKJFG
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.

8.312 Γ— 10⁹⁴(95-digit number)
83123969819329807048…48174778285890676201
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
8.312 Γ— 10⁹⁴(95-digit number)
83123969819329807048…48174778285890676201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.662 Γ— 10⁹⁡(96-digit number)
16624793963865961409…96349556571781352401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.324 Γ— 10⁹⁡(96-digit number)
33249587927731922819…92699113143562704801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.649 Γ— 10⁹⁡(96-digit number)
66499175855463845638…85398226287125409601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.329 Γ— 10⁹⁢(97-digit number)
13299835171092769127…70796452574250819201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.659 Γ— 10⁹⁢(97-digit number)
26599670342185538255…41592905148501638401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.319 Γ— 10⁹⁢(97-digit number)
53199340684371076511…83185810297003276801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.063 Γ— 10⁹⁷(98-digit number)
10639868136874215302…66371620594006553601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.127 Γ— 10⁹⁷(98-digit number)
21279736273748430604…32743241188013107201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.255 Γ— 10⁹⁷(98-digit number)
42559472547496861208…65486482376026214401
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:57,988,532 XPMΒ·at block #6,843,021 Β· updates every 60s
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