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Block #143,136

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2013, 10:48:29 AM Β· Difficulty 9.8375 Β· 6,667,137 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed3f6e911b1258f519daa3201293977339668238f522f10c2ecc846c0235c0cd
View on Chainz β†—

Height

#143,136

Difficulty

9.837476

Transactions

2

Size

732 B

Version

2

Bits

09d664db

Nonce

115,605

Timestamp

8/31/2013, 10:48:29 AM

Confirmations

6,667,137

Mined by

⛏️ XAV64KxAtGgKTadigYfszHFiyLGs7nd1fgf

Merkle Root

277399d90bbb41c05040fce4a4d47a140bf93a6fee7d57c738cff0ef87e31a4a
Transactions (2)
Coinbasee32c5e62d527bc…1e8c6613cd022c
1 in β†’ 1 out10.3300 XPM109 B
AV64KxAt…s7nd1fgf
127f999484ac96…176f2d83d7177f
4 in β†’ 1 out31.1800 XPM533 B
AQjAX9Vk…hTks6kYK
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.

7.750 Γ— 10⁹⁴(95-digit number)
77503947717576819252…71756255624217794561
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
7.750 Γ— 10⁹⁴(95-digit number)
77503947717576819252…71756255624217794561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.550 Γ— 10⁹⁡(96-digit number)
15500789543515363850…43512511248435589121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.100 Γ— 10⁹⁡(96-digit number)
31001579087030727700…87025022496871178241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.200 Γ— 10⁹⁡(96-digit number)
62003158174061455401…74050044993742356481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.240 Γ— 10⁹⁢(97-digit number)
12400631634812291080…48100089987484712961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.480 Γ— 10⁹⁢(97-digit number)
24801263269624582160…96200179974969425921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.960 Γ— 10⁹⁢(97-digit number)
49602526539249164321…92400359949938851841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.920 Γ— 10⁹⁢(97-digit number)
99205053078498328642…84800719899877703681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.984 Γ— 10⁹⁷(98-digit number)
19841010615699665728…69601439799755407361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.968 Γ— 10⁹⁷(98-digit number)
39682021231399331457…39202879599510814721
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:57,726,257 XPMΒ·at block #6,810,272 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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