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Block #1,630,869

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2016, 8:22:33 AM Β· Difficulty 10.6068 Β· 5,212,346 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
25edf0927cd7b29e6e8ceed410896d825ba8b023026a3205ec1fc643bbae72ca
View on Chainz β†—

Height

#1,630,869

Difficulty

10.606845

Transactions

1

Size

200 B

Version

2

Bits

0a9b5a31

Nonce

114,590,531

Timestamp

6/16/2016, 8:22:33 AM

Confirmations

5,212,346

Mined by

⛏️ P2SHAXPGDUfTWqmPWQm9MPZpWLivmTZg522f86

Merkle Root

d2701f87481fc6eeb3a18284486c6022491e104a67f10b7e2536d0fdee642c2f
Transactions (1)
Coinbased2701f87481fc6…36d0fdee642c2f
1 in β†’ 1 out8.8700 XPM110 B
AXPGDUfT…Zg522f86
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.

5.220 Γ— 10⁹³(94-digit number)
52209915321146433851…73415008745122499201
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
5.220 Γ— 10⁹³(94-digit number)
52209915321146433851…73415008745122499201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.044 Γ— 10⁹⁴(95-digit number)
10441983064229286770…46830017490244998401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.088 Γ— 10⁹⁴(95-digit number)
20883966128458573540…93660034980489996801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.176 Γ— 10⁹⁴(95-digit number)
41767932256917147080…87320069960979993601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.353 Γ— 10⁹⁴(95-digit number)
83535864513834294161…74640139921959987201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.670 Γ— 10⁹⁡(96-digit number)
16707172902766858832…49280279843919974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.341 Γ— 10⁹⁡(96-digit number)
33414345805533717664…98560559687839948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.682 Γ— 10⁹⁡(96-digit number)
66828691611067435329…97121119375679897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.336 Γ— 10⁹⁢(97-digit number)
13365738322213487065…94242238751359795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.673 Γ— 10⁹⁢(97-digit number)
26731476644426974131…88484477502719590401
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,990,093 XPMΒ·at block #6,843,214 Β· updates every 60s
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