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Block #42,779

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/14/2013, 7:23:30 PM Β· Difficulty 8.6236 Β· 6,752,098 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ef4b6e150f5130ca37f465e662ac03a23491bca614e7e1d36828088cc0712f10
View on Chainz β†—

Height

#42,779

Difficulty

8.623576

Transactions

1

Size

199 B

Version

2

Bits

089fa2a6

Nonce

90

Timestamp

7/14/2013, 7:23:30 PM

Confirmations

6,752,098

Mined by

⛏️ P2SHAerFQNGPeFHWC2PwEBw19KV4FSYEmuM8uZ

Merkle Root

25d5a2be5b5ad3afd8240b10bba67ccb428a4eb192fb56ae790137892007ced1
Transactions (1)
Coinbase25d5a2be5b5ad3…0137892007ced1
1 in β†’ 1 out13.4300 XPM109 B
AerFQNGP…YEmuM8uZ
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.

1.772 Γ— 10⁹⁴(95-digit number)
17722121579161622804…38394844635282978321
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
1.772 Γ— 10⁹⁴(95-digit number)
17722121579161622804…38394844635282978321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.544 Γ— 10⁹⁴(95-digit number)
35444243158323245608…76789689270565956641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.088 Γ— 10⁹⁴(95-digit number)
70888486316646491217…53579378541131913281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.417 Γ— 10⁹⁡(96-digit number)
14177697263329298243…07158757082263826561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.835 Γ— 10⁹⁡(96-digit number)
28355394526658596487…14317514164527653121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.671 Γ— 10⁹⁡(96-digit number)
56710789053317192974…28635028329055306241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.134 Γ— 10⁹⁢(97-digit number)
11342157810663438594…57270056658110612481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.268 Γ— 10⁹⁢(97-digit number)
22684315621326877189…14540113316221224961
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,603,050 XPMΒ·at block #6,794,876 Β· updates every 60s
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