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Block #150,618

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/5/2013, 3:53:23 AM Β· Difficulty 9.8588 Β· 6,652,905 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
010f9c6391b21262a76c0ad69f4fb09178fa37d77847594aa3480560be9bdad5
View on Chainz β†—

Height

#150,618

Difficulty

9.858806

Transactions

1

Size

199 B

Version

2

Bits

09dbdaaf

Nonce

19,286

Timestamp

9/5/2013, 3:53:23 AM

Confirmations

6,652,905

Mined by

⛏️ P2SHAJQ7bqzh8jMKwbhminzZ7vurTxoY2ANRaW

Merkle Root

39964a8ae0edc7d13ac238fdca8778befa3155b328152af30217768664099b88
Transactions (1)
Coinbase39964a8ae0edc7…17768664099b88
1 in β†’ 1 out10.2700 XPM109 B
AJQ7bqzh…oY2ANRaW
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.

7.458 Γ— 10⁹³(94-digit number)
74585620528356775217…08713267357931145321
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
7.458 Γ— 10⁹³(94-digit number)
74585620528356775217…08713267357931145321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.491 Γ— 10⁹⁴(95-digit number)
14917124105671355043…17426534715862290641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.983 Γ— 10⁹⁴(95-digit number)
29834248211342710086…34853069431724581281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.966 Γ— 10⁹⁴(95-digit number)
59668496422685420173…69706138863449162561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.193 Γ— 10⁹⁡(96-digit number)
11933699284537084034…39412277726898325121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.386 Γ— 10⁹⁡(96-digit number)
23867398569074168069…78824555453796650241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.773 Γ— 10⁹⁡(96-digit number)
47734797138148336139…57649110907593300481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.546 Γ— 10⁹⁡(96-digit number)
95469594276296672278…15298221815186600961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.909 Γ— 10⁹⁢(97-digit number)
19093918855259334455…30596443630373201921
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:57,672,211 XPMΒ·at block #6,803,522 Β· updates every 60s
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