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Block #2,130,016

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/24/2017, 3:37:54 AM Β· Difficulty 10.9094 Β· 4,711,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
cddf721aab90ca8dc8b9c4eda302dbe8b0153254bbe3126276351ebb7041fab6
View on Chainz β†—

Height

#2,130,016

Difficulty

10.909418

Transactions

1

Size

199 B

Version

2

Bits

0ae8cf9e

Nonce

604,642,039

Timestamp

5/24/2017, 3:37:54 AM

Confirmations

4,711,935

Mined by

⛏️ P2SHAaUrZAfaQVEw6WjWoSDqb2BeuHd13DLUr8

Merkle Root

c0ee65f2bc682e59bdbf3646d769445fdca5dcc9f0bb8135fe1682586834b347
Transactions (1)
Coinbasec0ee65f2bc682e…1682586834b347
1 in β†’ 1 out8.3900 XPM109 B
AaUrZAfa…d13DLUr8
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.

1.090 Γ— 10⁹⁴(95-digit number)
10902357197887138014…07676477124465960551
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
1.090 Γ— 10⁹⁴(95-digit number)
10902357197887138014…07676477124465960551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.180 Γ— 10⁹⁴(95-digit number)
21804714395774276028…15352954248931921101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.360 Γ— 10⁹⁴(95-digit number)
43609428791548552057…30705908497863842201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.721 Γ— 10⁹⁴(95-digit number)
87218857583097104115…61411816995727684401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.744 Γ— 10⁹⁡(96-digit number)
17443771516619420823…22823633991455368801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.488 Γ— 10⁹⁡(96-digit number)
34887543033238841646…45647267982910737601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.977 Γ— 10⁹⁡(96-digit number)
69775086066477683292…91294535965821475201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.395 Γ— 10⁹⁢(97-digit number)
13955017213295536658…82589071931642950401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.791 Γ— 10⁹⁢(97-digit number)
27910034426591073316…65178143863285900801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.582 Γ— 10⁹⁢(97-digit number)
55820068853182146633…30356287726571801601
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:57,979,988 XPMΒ·at block #6,841,950 Β· updates every 60s
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