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Block #2,091,338

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/28/2017, 10:39:14 AM Β· Difficulty 10.8726 Β· 4,739,779 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3699c0d4cb7db3c915f5cd9d604db25fbdaa2a3958787a93630d31e2111ce8a7
View on Chainz β†—

Height

#2,091,338

Difficulty

10.872609

Transactions

1

Size

209 B

Version

2

Bits

0adf6348

Nonce

68,786,152

Timestamp

4/28/2017, 10:39:14 AM

Confirmations

4,739,779

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

e7a21a14a8ea6b9c8e1b7d40432c1160c7985cfa6fe78413d3fea82556215d75
Transactions (1)
Coinbasee7a21a14a8ea6b…fea82556215d75
1 in β†’ 1 out8.4500 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.334 Γ— 10⁹⁷(98-digit number)
13343694078112776988…46475354110911908481
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
1.334 Γ— 10⁹⁷(98-digit number)
13343694078112776988…46475354110911908481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.668 Γ— 10⁹⁷(98-digit number)
26687388156225553976…92950708221823816961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.337 Γ— 10⁹⁷(98-digit number)
53374776312451107952…85901416443647633921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.067 Γ— 10⁹⁸(99-digit number)
10674955262490221590…71802832887295267841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.134 Γ— 10⁹⁸(99-digit number)
21349910524980443181…43605665774590535681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.269 Γ— 10⁹⁸(99-digit number)
42699821049960886362…87211331549181071361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.539 Γ— 10⁹⁸(99-digit number)
85399642099921772724…74422663098362142721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.707 Γ— 10⁹⁹(100-digit number)
17079928419984354544…48845326196724285441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.415 Γ— 10⁹⁹(100-digit number)
34159856839968709089…97690652393448570881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.831 Γ— 10⁹⁹(100-digit number)
68319713679937418179…95381304786897141761
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:57,893,081 XPMΒ·at block #6,831,116 Β· updates every 60s
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