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Block #2,138,962

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/31/2017, 8:16:56 AM Β· Difficulty 10.8804 Β· 4,692,972 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5a3343ad4c908f5d990977debf36e18d42d9da9b3fc9b37fd60c4af3a6f3b231
View on Chainz β†—

Height

#2,138,962

Difficulty

10.880449

Transactions

1

Size

199 B

Version

2

Bits

0ae16515

Nonce

443,712,689

Timestamp

5/31/2017, 8:16:56 AM

Confirmations

4,692,972

Mined by

⛏️ P2SHAePDmvigFcNT4ddVcTJB5pbgtZUJzPjgta

Merkle Root

b438e675e8e5de28c253b91a7deb82379e9d786e958dd1d5c1d32312b8dc1af5
Transactions (1)
Coinbaseb438e675e8e5de…d32312b8dc1af5
1 in β†’ 1 out8.4300 XPM109 B
AePDmvig…UJzPjgta
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.

5.166 Γ— 10⁹⁴(95-digit number)
51666901166746551656…73486118017641493561
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
5.166 Γ— 10⁹⁴(95-digit number)
51666901166746551656…73486118017641493561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.033 Γ— 10⁹⁡(96-digit number)
10333380233349310331…46972236035282987121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.066 Γ— 10⁹⁡(96-digit number)
20666760466698620662…93944472070565974241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.133 Γ— 10⁹⁡(96-digit number)
41333520933397241325…87888944141131948481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.266 Γ— 10⁹⁡(96-digit number)
82667041866794482650…75777888282263896961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.653 Γ— 10⁹⁢(97-digit number)
16533408373358896530…51555776564527793921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.306 Γ— 10⁹⁢(97-digit number)
33066816746717793060…03111553129055587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.613 Γ— 10⁹⁢(97-digit number)
66133633493435586120…06223106258111175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.322 Γ— 10⁹⁷(98-digit number)
13226726698687117224…12446212516222351361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.645 Γ— 10⁹⁷(98-digit number)
26453453397374234448…24892425032444702721
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:57,899,589 XPMΒ·at block #6,831,933 Β· updates every 60s
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