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Block #98,309

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2013, 4:26:44 AM Β· Difficulty 9.3375 Β· 6,719,673 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5edd35f9abb673e23ce51d27aa2e8bbb16ae0c510137c60096bcccd271c9c23b
View on Chainz β†—

Height

#98,309

Difficulty

9.337458

Transactions

1

Size

200 B

Version

2

Bits

095663ab

Nonce

14,835

Timestamp

8/5/2013, 4:26:44 AM

Confirmations

6,719,673

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

ba0a33a97eca854abfe0633058a5e85fc11c2177f98445e51b0d1bd4a20554ac
Transactions (1)
Coinbaseba0a33a97eca85…0d1bd4a20554ac
1 in β†’ 1 out11.4500 XPM109 B
AXvMMum1…y1ajpFRb
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.

4.776 Γ— 10⁹⁷(98-digit number)
47763818640698147834…68587423745294810631
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
4.776 Γ— 10⁹⁷(98-digit number)
47763818640698147834…68587423745294810631
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.552 Γ— 10⁹⁷(98-digit number)
95527637281396295669…37174847490589621261
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.910 Γ— 10⁹⁸(99-digit number)
19105527456279259133…74349694981179242521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.821 Γ— 10⁹⁸(99-digit number)
38211054912558518267…48699389962358485041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.642 Γ— 10⁹⁸(99-digit number)
76422109825117036535…97398779924716970081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.528 Γ— 10⁹⁹(100-digit number)
15284421965023407307…94797559849433940161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.056 Γ— 10⁹⁹(100-digit number)
30568843930046814614…89595119698867880321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.113 Γ— 10⁹⁹(100-digit number)
61137687860093629228…79190239397735760641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.222 Γ— 10¹⁰⁰(101-digit number)
12227537572018725845…58380478795471521281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,787,927 XPMΒ·at block #6,817,981 Β· updates every 60s
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