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Block #145,728

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/2/2013, 2:01:05 AM Β· Difficulty 9.8451 Β· 6,663,869 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
568a78f15e7e173f5575fd81c17b57a9efbe7b0c967f5eb40eb6156793fa4bc7
View on Chainz β†—

Height

#145,728

Difficulty

9.845053

Transactions

1

Size

198 B

Version

2

Bits

09d85564

Nonce

285,263

Timestamp

9/2/2013, 2:01:05 AM

Confirmations

6,663,869

Mined by

⛏️ P2SHANsvDN5KDUBF83BQczFTri757NjwzDHo7V

Merkle Root

5c62cb842bfe6d3b59dc9b79669141c923f60ae348c6e928adceae0d21596ec9
Transactions (1)
Coinbase5c62cb842bfe6d…ceae0d21596ec9
1 in β†’ 1 out10.3000 XPM109 B
ANsvDN5K…jwzDHo7V
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.

8.258 Γ— 10⁹²(93-digit number)
82587144540772298801…05712077418901493901
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
8.258 Γ— 10⁹²(93-digit number)
82587144540772298801…05712077418901493901
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.651 Γ— 10⁹³(94-digit number)
16517428908154459760…11424154837802987801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.303 Γ— 10⁹³(94-digit number)
33034857816308919520…22848309675605975601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.606 Γ— 10⁹³(94-digit number)
66069715632617839041…45696619351211951201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.321 Γ— 10⁹⁴(95-digit number)
13213943126523567808…91393238702423902401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.642 Γ— 10⁹⁴(95-digit number)
26427886253047135616…82786477404847804801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.285 Γ— 10⁹⁴(95-digit number)
52855772506094271233…65572954809695609601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.057 Γ— 10⁹⁡(96-digit number)
10571154501218854246…31145909619391219201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.114 Γ— 10⁹⁡(96-digit number)
21142309002437708493…62291819238782438401
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:57,720,850 XPMΒ·at block #6,809,596 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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