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Block #58,326

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/17/2013, 8:05:36 PM Β· Difficulty 8.9593 Β· 6,747,566 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0d5c129cf11879210e8a1b641db98c8c535a18419479d8c55f88d0b21d5b8ccf
View on Chainz β†—

Height

#58,326

Difficulty

8.959288

Transactions

2

Size

871 B

Version

2

Bits

08f593ea

Nonce

630

Timestamp

7/17/2013, 8:05:36 PM

Confirmations

6,747,566

Mined by

⛏️ P2SHASg92u69JSVAhWZXCWo8cCRivnNxw7Cxdk

Merkle Root

a7c537ba89f63bf4b24ac041cad7afb55c78675fb6861ee4de74db4cedd03170
Transactions (2)
Coinbase98f3e1406abd92…5b00e628047696
1 in β†’ 1 out12.4500 XPM110 B
ASg92u69…Nxw7Cxdk
f21bcac20d53ec…a0f52876a2d65a
4 in β†’ 2 out228.0833 XPM670 B
ATnuqLLQ…6uPuUpUTAea5qFPK…z2VFU5nR
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.

1.109 Γ— 10⁹⁷(98-digit number)
11094566376523280618…78786224579836360401
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
1.109 Γ— 10⁹⁷(98-digit number)
11094566376523280618…78786224579836360401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.218 Γ— 10⁹⁷(98-digit number)
22189132753046561237…57572449159672720801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.437 Γ— 10⁹⁷(98-digit number)
44378265506093122474…15144898319345441601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.875 Γ— 10⁹⁷(98-digit number)
88756531012186244948…30289796638690883201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.775 Γ— 10⁹⁸(99-digit number)
17751306202437248989…60579593277381766401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.550 Γ— 10⁹⁸(99-digit number)
35502612404874497979…21159186554763532801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.100 Γ— 10⁹⁸(99-digit number)
71005224809748995958…42318373109527065601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.420 Γ— 10⁹⁹(100-digit number)
14201044961949799191…84636746219054131201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.840 Γ— 10⁹⁹(100-digit number)
28402089923899598383…69273492438108262401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.680 Γ— 10⁹⁹(100-digit number)
56804179847799196767…38546984876216524801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.136 Γ— 10¹⁰⁰(101-digit number)
11360835969559839353…77093969752433049601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,691,222 XPMΒ·at block #6,805,891 Β· updates every 60s
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