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Block #2,634,250

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2018, 7:54:33 PM Β· Difficulty 11.2327 Β· 4,206,442 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1bf61753b6a102c4ba5fb341551e552a49968c42d543648006ecd5c25d7d196e
View on Chainz β†—

Height

#2,634,250

Difficulty

11.232722

Transactions

1

Size

198 B

Version

2

Bits

0b3b93a6

Nonce

281,514,313

Timestamp

4/28/2018, 7:54:33 PM

Confirmations

4,206,442

Mined by

⛏️ P2SHAWXWCW24Q4SnnEyZgGwF9cGv6oe5W36C1N

Merkle Root

b28299b6e872d46a4c805da4f982dfe906cb4d4d93eb36ef7b6a1309a995b85a
Transactions (1)
Coinbaseb28299b6e872d4…6a1309a995b85a
1 in β†’ 1 out7.9100 XPM109 B
AWXWCW24…e5W36C1N
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.

3.053 Γ— 10⁹³(94-digit number)
30536062863079222561…78879365507449986561
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
3.053 Γ— 10⁹³(94-digit number)
30536062863079222561…78879365507449986561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
6.107 Γ— 10⁹³(94-digit number)
61072125726158445123…57758731014899973121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.221 Γ— 10⁹⁴(95-digit number)
12214425145231689024…15517462029799946241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.442 Γ— 10⁹⁴(95-digit number)
24428850290463378049…31034924059599892481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.885 Γ— 10⁹⁴(95-digit number)
48857700580926756098…62069848119199784961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.771 Γ— 10⁹⁴(95-digit number)
97715401161853512197…24139696238399569921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.954 Γ— 10⁹⁡(96-digit number)
19543080232370702439…48279392476799139841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.908 Γ— 10⁹⁡(96-digit number)
39086160464741404879…96558784953598279681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.817 Γ— 10⁹⁡(96-digit number)
78172320929482809758…93117569907196559361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.563 Γ— 10⁹⁢(97-digit number)
15634464185896561951…86235139814393118721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.126 Γ— 10⁹⁢(97-digit number)
31268928371793123903…72470279628786237441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,969,876 XPMΒ·at block #6,840,691 Β· updates every 60s
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