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Block #2,118,692

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2017, 6:48:00 AM Β· Difficulty 10.9092 Β· 4,691,263 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
82f4085a31238731530180eec9542498435d3fc2fe61beb377e33b40760b18a9
View on Chainz β†—

Height

#2,118,692

Difficulty

10.909203

Transactions

2

Size

1.10 KB

Version

2

Bits

0ae8c183

Nonce

1,319,160,751

Timestamp

5/16/2017, 6:48:00 AM

Confirmations

4,691,263

Mined by

⛏️ P2SHAc6jgZQVeffy6mpAXPVDDPfVUtKa7p5Be8

Merkle Root

be60aaca5cf5e06b7b476ae8db9d6f273d453a28d31858f3b59b33dd9e7931d5
Transactions (2)
Coinbasee28fdde0b56581…dd7aaa9f5bd16f
1 in β†’ 1 out8.4100 XPM109 B
Ac6jgZQV…Ka7p5Be8
410ac960367be0…6f7dfa038a051d
6 in β†’ 1 out3071.9415 XPM931 B
AWFYixUG…4nL4F5Bp
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.

9.020 Γ— 10⁹⁢(97-digit number)
90206685835799219341…61307008527118167041
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
9.020 Γ— 10⁹⁢(97-digit number)
90206685835799219341…61307008527118167041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.804 Γ— 10⁹⁷(98-digit number)
18041337167159843868…22614017054236334081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.608 Γ— 10⁹⁷(98-digit number)
36082674334319687736…45228034108472668161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.216 Γ— 10⁹⁷(98-digit number)
72165348668639375473…90456068216945336321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.443 Γ— 10⁹⁸(99-digit number)
14433069733727875094…80912136433890672641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.886 Γ— 10⁹⁸(99-digit number)
28866139467455750189…61824272867781345281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.773 Γ— 10⁹⁸(99-digit number)
57732278934911500378…23648545735562690561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.154 Γ— 10⁹⁹(100-digit number)
11546455786982300075…47297091471125381121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.309 Γ— 10⁹⁹(100-digit number)
23092911573964600151…94594182942250762241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.618 Γ— 10⁹⁹(100-digit number)
46185823147929200302…89188365884501524481
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:57,723,721 XPMΒ·at block #6,809,954 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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