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Block #2,859,965

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/29/2018, 3:47:14 PM Β· Difficulty 11.6745 Β· 3,982,261 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
477d4e4d3dcd75b8ba492045dd00b176a5500c0ee4c4da9a7033408b1e5e0cbe
View on Chainz β†—

Height

#2,859,965

Difficulty

11.674523

Transactions

1

Size

200 B

Version

2

Bits

0bacad83

Nonce

154,294,267

Timestamp

9/29/2018, 3:47:14 PM

Confirmations

3,982,261

Mined by

⛏️ P2SHAWZzzSPtwHz1KgcYwAg6o1jAfAbsuDmeyo

Merkle Root

736d19596b430347ddfc540d7a6934f14182ea02a7b1ea2d9a51a45dd9ce0fcf
Transactions (1)
Coinbase736d19596b4303…51a45dd9ce0fcf
1 in β†’ 1 out7.3200 XPM110 B
AWZzzSPt…bsuDmeyo
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.

5.650 Γ— 10⁹³(94-digit number)
56506030337520805203…32695309411203076141
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
5.650 Γ— 10⁹³(94-digit number)
56506030337520805203…32695309411203076141
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.130 Γ— 10⁹⁴(95-digit number)
11301206067504161040…65390618822406152281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.260 Γ— 10⁹⁴(95-digit number)
22602412135008322081…30781237644812304561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.520 Γ— 10⁹⁴(95-digit number)
45204824270016644162…61562475289624609121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.040 Γ— 10⁹⁴(95-digit number)
90409648540033288325…23124950579249218241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.808 Γ— 10⁹⁡(96-digit number)
18081929708006657665…46249901158498436481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.616 Γ— 10⁹⁡(96-digit number)
36163859416013315330…92499802316996872961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.232 Γ— 10⁹⁡(96-digit number)
72327718832026630660…84999604633993745921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.446 Γ— 10⁹⁢(97-digit number)
14465543766405326132…69999209267987491841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.893 Γ— 10⁹⁢(97-digit number)
28931087532810652264…39998418535974983681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.786 Γ— 10⁹⁢(97-digit number)
57862175065621304528…79996837071949967361
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:57,982,206 XPMΒ·at block #6,842,225 Β· updates every 60s
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