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Block #2,134,071

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/26/2017, 11:56:55 PM Β· Difficulty 10.9087 Β· 4,710,759 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f0de6dde9a41f007b9c91a5a467e9a74b5eaa64c100715ba420de4674a0d700c
View on Chainz β†—

Height

#2,134,071

Difficulty

10.908736

Transactions

1

Size

200 B

Version

2

Bits

0ae8a2f2

Nonce

464,266,430

Timestamp

5/26/2017, 11:56:55 PM

Confirmations

4,710,759

Mined by

⛏️ P2SHAesQ2QxJAGPekxxUspDgAf5Y5NFwSKahKm

Merkle Root

7ae21c884af867eae3d1db24bac27dee6241112274357629df2b891542e4d3ac
Transactions (1)
Coinbase7ae21c884af867…2b891542e4d3ac
1 in β†’ 1 out8.3900 XPM109 B
AesQ2QxJ…FwSKahKm
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.

8.434 Γ— 10⁹⁡(96-digit number)
84346301505502404789…93618118527166504961
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
8.434 Γ— 10⁹⁡(96-digit number)
84346301505502404789…93618118527166504961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.686 Γ— 10⁹⁢(97-digit number)
16869260301100480957…87236237054333009921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.373 Γ— 10⁹⁢(97-digit number)
33738520602200961915…74472474108666019841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.747 Γ— 10⁹⁢(97-digit number)
67477041204401923831…48944948217332039681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.349 Γ— 10⁹⁷(98-digit number)
13495408240880384766…97889896434664079361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.699 Γ— 10⁹⁷(98-digit number)
26990816481760769532…95779792869328158721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.398 Γ— 10⁹⁷(98-digit number)
53981632963521539065…91559585738656317441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.079 Γ— 10⁹⁸(99-digit number)
10796326592704307813…83119171477312634881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.159 Γ— 10⁹⁸(99-digit number)
21592653185408615626…66238342954625269761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.318 Γ— 10⁹⁸(99-digit number)
43185306370817231252…32476685909250539521
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:58,003,049 XPMΒ·at block #6,844,829 Β· updates every 60s
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