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Block #158,969

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/10/2013, 7:09:45 PM Β· Difficulty 9.8656 Β· 6,649,530 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9533a7f48e3fcca533472956d605d9ca1ed70ac4295ca993b4ce1fd51d93a5e6
View on Chainz β†—

Height

#158,969

Difficulty

9.865615

Transactions

2

Size

619 B

Version

2

Bits

09dd98f6

Nonce

522,322

Timestamp

9/10/2013, 7:09:45 PM

Confirmations

6,649,530

Mined by

⛏️ P2SHAM9R37qPciuhUNYvwcMUHTUsnwhm8dCX8m

Merkle Root

eaa24bd6e548a4f6b0fa628ddeb67efe08aaef904f76a94f8aae32bcd02fe77f
Transactions (2)
Coinbaseeeb70af6a92c87…d6861eae2bebfb
1 in β†’ 1 out10.2700 XPM109 B
AM9R37qP…hm8dCX8m
775b25188da9de…40eceb644a2f4b
3 in β†’ 1 out30.7900 XPM421 B
AXMczY6e…mKYm2rod
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.

1.120 Γ— 10⁹²(93-digit number)
11200172194995960535…98277776310942489601
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
1.120 Γ— 10⁹²(93-digit number)
11200172194995960535…98277776310942489601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.240 Γ— 10⁹²(93-digit number)
22400344389991921070…96555552621884979201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.480 Γ— 10⁹²(93-digit number)
44800688779983842141…93111105243769958401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.960 Γ— 10⁹²(93-digit number)
89601377559967684283…86222210487539916801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.792 Γ— 10⁹³(94-digit number)
17920275511993536856…72444420975079833601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.584 Γ— 10⁹³(94-digit number)
35840551023987073713…44888841950159667201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.168 Γ— 10⁹³(94-digit number)
71681102047974147426…89777683900319334401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.433 Γ— 10⁹⁴(95-digit number)
14336220409594829485…79555367800638668801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.867 Γ— 10⁹⁴(95-digit number)
28672440819189658970…59110735601277337601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.734 Γ— 10⁹⁴(95-digit number)
57344881638379317941…18221471202554675201
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:57,712,045 XPMΒ·at block #6,808,498 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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