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Block #2,132,769

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 12:48:21 AM Β· Difficulty 10.9103 Β· 4,709,307 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5655ea4367aaddfac106e36a135865efb5b7ba0fd7d6bb084ec26f534897d319
View on Chainz β†—

Height

#2,132,769

Difficulty

10.910285

Transactions

1

Size

199 B

Version

2

Bits

0ae9086c

Nonce

1,291,307,392

Timestamp

5/26/2017, 12:48:21 AM

Confirmations

4,709,307

Mined by

⛏️ P2SHAVQg6j1qQjYmr37WGu6JqPtkt7ZvAbZqpU

Merkle Root

2e79b60a0dd1688eea1b3866562cd5dbde5e5c431d6e9f03b1d6e1cddf07acd0
Transactions (1)
Coinbase2e79b60a0dd168…d6e1cddf07acd0
1 in β†’ 1 out8.3900 XPM109 B
AVQg6j1q…ZvAbZqpU
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.

5.409 Γ— 10⁹⁡(96-digit number)
54091487786435057373…55066921443429756161
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
5.409 Γ— 10⁹⁡(96-digit number)
54091487786435057373…55066921443429756161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.081 Γ— 10⁹⁢(97-digit number)
10818297557287011474…10133842886859512321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.163 Γ— 10⁹⁢(97-digit number)
21636595114574022949…20267685773719024641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.327 Γ— 10⁹⁢(97-digit number)
43273190229148045898…40535371547438049281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.654 Γ— 10⁹⁢(97-digit number)
86546380458296091797…81070743094876098561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.730 Γ— 10⁹⁷(98-digit number)
17309276091659218359…62141486189752197121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.461 Γ— 10⁹⁷(98-digit number)
34618552183318436718…24282972379504394241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.923 Γ— 10⁹⁷(98-digit number)
69237104366636873437…48565944759008788481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.384 Γ— 10⁹⁸(99-digit number)
13847420873327374687…97131889518017576961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.769 Γ— 10⁹⁸(99-digit number)
27694841746654749375…94263779036035153921
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:57,980,993 XPMΒ·at block #6,842,075 Β· updates every 60s
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