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Block #142,516

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2013, 12:28:40 AM Β· Difficulty 9.8374 Β· 6,660,115 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
13cfd7d89b7e983a3b273eed16f805a72b8df21ea0d7e2faa8e23928d62def16
View on Chainz β†—

Height

#142,516

Difficulty

9.837420

Transactions

1

Size

198 B

Version

2

Bits

09d66128

Nonce

32,336

Timestamp

8/31/2013, 12:28:40 AM

Confirmations

6,660,115

Mined by

⛏️ P2SHAZ8Ujr32krTeTQYFNnSTUjH7625B7ssqDY

Merkle Root

ac789a86ffea52b86053a71b7ae6ada78f72c9681c903684fd8410d927707771
Transactions (1)
Coinbaseac789a86ffea52…8410d927707771
1 in β†’ 1 out10.3200 XPM109 B
AZ8Ujr32…5B7ssqDY
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.

1.669 Γ— 10⁹²(93-digit number)
16692535003037150979…23917232278891903801
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
1.669 Γ— 10⁹²(93-digit number)
16692535003037150979…23917232278891903801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.338 Γ— 10⁹²(93-digit number)
33385070006074301958…47834464557783807601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.677 Γ— 10⁹²(93-digit number)
66770140012148603917…95668929115567615201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.335 Γ— 10⁹³(94-digit number)
13354028002429720783…91337858231135230401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.670 Γ— 10⁹³(94-digit number)
26708056004859441567…82675716462270460801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.341 Γ— 10⁹³(94-digit number)
53416112009718883134…65351432924540921601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.068 Γ— 10⁹⁴(95-digit number)
10683222401943776626…30702865849081843201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.136 Γ— 10⁹⁴(95-digit number)
21366444803887553253…61405731698163686401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.273 Γ— 10⁹⁴(95-digit number)
42732889607775106507…22811463396327372801
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:57,665,063 XPMΒ·at block #6,802,630 Β· updates every 60s
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