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Block #1,678,432

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/18/2016, 12:50:32 PM Β· Difficulty 10.6930 Β· 5,161,644 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
406c306223e80b1ff1b31754c861c43204bfb783b21411a4428be581021296b2
View on Chainz β†—

Height

#1,678,432

Difficulty

10.693012

Transactions

1

Size

199 B

Version

2

Bits

0ab1693a

Nonce

178,986,994

Timestamp

7/18/2016, 12:50:32 PM

Confirmations

5,161,644

Mined by

⛏️ P2SHAJWS4SjgSmVYeyks8t5kQ5hDBvmXXooZQE

Merkle Root

15d38dd8ff22689b6ca582119904b44ce0b8c0b58a9e8ac72481a9b7f0a38874
Transactions (1)
Coinbase15d38dd8ff2268…81a9b7f0a38874
1 in β†’ 1 out8.7300 XPM109 B
AJWS4Sjg…mXXooZQE
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.

2.462 Γ— 10⁹⁡(96-digit number)
24623024846407545889…46078451589511868201
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
2.462 Γ— 10⁹⁡(96-digit number)
24623024846407545889…46078451589511868201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.924 Γ— 10⁹⁡(96-digit number)
49246049692815091778…92156903179023736401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.849 Γ— 10⁹⁡(96-digit number)
98492099385630183557…84313806358047472801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.969 Γ— 10⁹⁢(97-digit number)
19698419877126036711…68627612716094945601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.939 Γ— 10⁹⁢(97-digit number)
39396839754252073423…37255225432189891201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.879 Γ— 10⁹⁢(97-digit number)
78793679508504146846…74510450864379782401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.575 Γ— 10⁹⁷(98-digit number)
15758735901700829369…49020901728759564801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.151 Γ— 10⁹⁷(98-digit number)
31517471803401658738…98041803457519129601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.303 Γ— 10⁹⁷(98-digit number)
63034943606803317477…96083606915038259201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.260 Γ— 10⁹⁸(99-digit number)
12606988721360663495…92167213830076518401
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:57,964,915 XPMΒ·at block #6,840,075 Β· updates every 60s
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