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Block #178,539

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/24/2013, 11:32:14 AM Β· Difficulty 9.8630 Β· 6,665,142 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
45eeb331fe27e88460934f04d182cc82e98244302a30e4341ed43310232cd03b
View on Chainz β†—

Height

#178,539

Difficulty

9.863034

Transactions

2

Size

391 B

Version

2

Bits

09dcefcb

Nonce

159,709

Timestamp

9/24/2013, 11:32:14 AM

Confirmations

6,665,142

Mined by

⛏️ P2SHANqcKqgHvu11AkCJVnDhcWYabdjns52FdU

Merkle Root

2b42ba22ffd8059095ee810c2f12125ae4e9db99b8945a084fd150c39cb8aec7
Transactions (2)
Coinbasef0160a590f17a8…0b04be653b73c6
1 in β†’ 1 out10.2700 XPM109 B
ANqcKqgH…jns52FdU
7f5504ffb1fa48…3ccb4002cf98a9
1 in β†’ 1 out149.9900 XPM191 B
AGeif5Fs…o1sGXdJ5
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.

1.018 Γ— 10⁹⁢(97-digit number)
10185352494001337119…05681549483828377601
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
1.018 Γ— 10⁹⁢(97-digit number)
10185352494001337119…05681549483828377601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.037 Γ— 10⁹⁢(97-digit number)
20370704988002674238…11363098967656755201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.074 Γ— 10⁹⁢(97-digit number)
40741409976005348476…22726197935313510401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.148 Γ— 10⁹⁢(97-digit number)
81482819952010696952…45452395870627020801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.629 Γ— 10⁹⁷(98-digit number)
16296563990402139390…90904791741254041601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.259 Γ— 10⁹⁷(98-digit number)
32593127980804278781…81809583482508083201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.518 Γ— 10⁹⁷(98-digit number)
65186255961608557562…63619166965016166401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.303 Γ— 10⁹⁸(99-digit number)
13037251192321711512…27238333930032332801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.607 Γ— 10⁹⁸(99-digit number)
26074502384643423024…54476667860064665601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.214 Γ— 10⁹⁸(99-digit number)
52149004769286846049…08953335720129331201
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:57,993,821 XPMΒ·at block #6,843,680 Β· updates every 60s
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