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Block #77,660

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/22/2013, 12:12:00 PM Β· Difficulty 9.1884 Β· 6,718,385 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8b0869772434ef7e29c527a5752e3c3ceac6de25aa4b1ed3d5cfa42027f0c8d7
View on Chainz β†—

Height

#77,660

Difficulty

9.188416

Transactions

1

Size

199 B

Version

2

Bits

09303c02

Nonce

4

Timestamp

7/22/2013, 12:12:00 PM

Confirmations

6,718,385

Mined by

⛏️ P2SHAS4Pf5oLcWa2Bm61YMMFth8zvCfdaGq2mN

Merkle Root

ec0dcba0d700356bc12f99828401be587702859ab16142a98b88bbeb3e4fb7de
Transactions (1)
Coinbaseec0dcba0d70035…88bbeb3e4fb7de
1 in β†’ 1 out11.8300 XPM110 B
AS4Pf5oL…fdaGq2mN
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.

9.467 Γ— 10⁹¹(92-digit number)
94672776909521971675…14156836761505723351
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
9.467 Γ— 10⁹¹(92-digit number)
94672776909521971675…14156836761505723351
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.893 Γ— 10⁹²(93-digit number)
18934555381904394335…28313673523011446701
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.786 Γ— 10⁹²(93-digit number)
37869110763808788670…56627347046022893401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.573 Γ— 10⁹²(93-digit number)
75738221527617577340…13254694092045786801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.514 Γ— 10⁹³(94-digit number)
15147644305523515468…26509388184091573601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.029 Γ— 10⁹³(94-digit number)
30295288611047030936…53018776368183147201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.059 Γ— 10⁹³(94-digit number)
60590577222094061872…06037552736366294401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.211 Γ— 10⁹⁴(95-digit number)
12118115444418812374…12075105472732588801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.423 Γ— 10⁹⁴(95-digit number)
24236230888837624749…24150210945465177601
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:57,612,453 XPMΒ·at block #6,796,044 Β· updates every 60s
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