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Block #2,079,074

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/20/2017, 7:17:19 AM Β· Difficulty 10.8578 Β· 4,751,928 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f12c23a86d71f18a2804b03c4ae6a22e4f56026b400a23216ac64e085bd08179
View on Chainz β†—

Height

#2,079,074

Difficulty

10.857753

Transactions

1

Size

209 B

Version

2

Bits

0adb95b2

Nonce

99,385,575

Timestamp

4/20/2017, 7:17:19 AM

Confirmations

4,751,928

Mined by

⛏️ P2SHAM6GYpjwZFjhLNzHZAfmRp8jwiaw86QDtR

Merkle Root

a4e576a033003d263e7f25b95b72e6fe702089d3b05362546931e7dfba41c5d9
Transactions (1)
Coinbasea4e576a033003d…31e7dfba41c5d9
1 in β†’ 1 out8.4700 XPM118 B
AM6GYpjw…aw86QDtR
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.

7.615 Γ— 10⁹⁡(96-digit number)
76157970084836211200…75603447174627122401
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
7.615 Γ— 10⁹⁡(96-digit number)
76157970084836211200…75603447174627122401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.523 Γ— 10⁹⁢(97-digit number)
15231594016967242240…51206894349254244801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.046 Γ— 10⁹⁢(97-digit number)
30463188033934484480…02413788698508489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.092 Γ— 10⁹⁢(97-digit number)
60926376067868968960…04827577397016979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.218 Γ— 10⁹⁷(98-digit number)
12185275213573793792…09655154794033958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.437 Γ— 10⁹⁷(98-digit number)
24370550427147587584…19310309588067916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.874 Γ— 10⁹⁷(98-digit number)
48741100854295175168…38620619176135833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.748 Γ— 10⁹⁷(98-digit number)
97482201708590350337…77241238352271667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.949 Γ— 10⁹⁸(99-digit number)
19496440341718070067…54482476704543334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.899 Γ— 10⁹⁸(99-digit number)
38992880683436140134…08964953409086668801
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:57,892,157 XPMΒ·at block #6,831,001 Β· updates every 60s
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