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Block #2,132,167

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/25/2017, 2:57:24 PM Β· Difficulty 10.9100 Β· 4,708,860 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c1907342dfbcd39acfd7c206bdd5b91b168514d23fd15265569d8173d88f6e2f
View on Chainz β†—

Height

#2,132,167

Difficulty

10.910043

Transactions

1

Size

199 B

Version

2

Bits

0ae8f895

Nonce

302,191,802

Timestamp

5/25/2017, 2:57:24 PM

Confirmations

4,708,860

Mined by

⛏️ P2SHAXFARg182xZ4QcJmmaJhkAi9UT2W3ZHoWG

Merkle Root

3a78712031f1fa9789ec8f187edf1ed6680b84924a4f5df3b1cb9b44f9d3e30f
Transactions (1)
Coinbase3a78712031f1fa…cb9b44f9d3e30f
1 in β†’ 1 out8.3900 XPM109 B
AXFARg18…2W3ZHoWG
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.

9.215 Γ— 10⁹⁴(95-digit number)
92153320358397622286…08928432526730769921
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
9.215 Γ— 10⁹⁴(95-digit number)
92153320358397622286…08928432526730769921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.843 Γ— 10⁹⁡(96-digit number)
18430664071679524457…17856865053461539841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.686 Γ— 10⁹⁡(96-digit number)
36861328143359048914…35713730106923079681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.372 Γ— 10⁹⁡(96-digit number)
73722656286718097829…71427460213846159361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.474 Γ— 10⁹⁢(97-digit number)
14744531257343619565…42854920427692318721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.948 Γ— 10⁹⁢(97-digit number)
29489062514687239131…85709840855384637441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.897 Γ— 10⁹⁢(97-digit number)
58978125029374478263…71419681710769274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.179 Γ— 10⁹⁷(98-digit number)
11795625005874895652…42839363421538549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.359 Γ— 10⁹⁷(98-digit number)
23591250011749791305…85678726843077099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.718 Γ— 10⁹⁷(98-digit number)
47182500023499582610…71357453686154199041
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:57,972,574 XPMΒ·at block #6,841,026 Β· updates every 60s
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