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Block #2,639,115

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/30/2018, 1:04:49 PM Β· Difficulty 11.5230 Β· 4,193,451 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
940446fcd265c8a3abcc41d1dbac18889b43f8a08b63e00930442c31f8f67986
View on Chainz β†—

Height

#2,639,115

Difficulty

11.522951

Transactions

1

Size

200 B

Version

2

Bits

0b85e01d

Nonce

1,648,189

Timestamp

4/30/2018, 1:04:49 PM

Confirmations

4,193,451

Mined by

⛏️ P2SHAXCCNm2e1StD4rf9FmSVfLwGQVazxJjUV3

Merkle Root

cdbfc0f38bcc0d1a790b92da82895fe84b97e10d05a9533f112eb0917723a409
Transactions (1)
Coinbasecdbfc0f38bcc0d…2eb0917723a409
1 in β†’ 1 out7.5200 XPM110 B
AXCCNm2e…azxJjUV3
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.

1.367 Γ— 10⁹⁡(96-digit number)
13671572349406873934…42165278870257975971
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
1.367 Γ— 10⁹⁡(96-digit number)
13671572349406873934…42165278870257975971
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.734 Γ— 10⁹⁡(96-digit number)
27343144698813747868…84330557740515951941
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.468 Γ— 10⁹⁡(96-digit number)
54686289397627495736…68661115481031903881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.093 Γ— 10⁹⁢(97-digit number)
10937257879525499147…37322230962063807761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.187 Γ— 10⁹⁢(97-digit number)
21874515759050998294…74644461924127615521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.374 Γ— 10⁹⁢(97-digit number)
43749031518101996589…49288923848255231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.749 Γ— 10⁹⁢(97-digit number)
87498063036203993178…98577847696510462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.749 Γ— 10⁹⁷(98-digit number)
17499612607240798635…97155695393020924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.499 Γ— 10⁹⁷(98-digit number)
34999225214481597271…94311390786041848321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.999 Γ— 10⁹⁷(98-digit number)
69998450428963194542…88622781572083696641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.399 Γ— 10⁹⁸(99-digit number)
13999690085792638908…77245563144167393281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,904,686 XPMΒ·at block #6,832,565 Β· updates every 60s
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