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Block #1,611,372

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/2/2016, 7:24:05 PM Β· Difficulty 10.6059 Β· 5,231,643 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
57af209d3c378e34c7914e5e33506ba7c6dc4aaceb8ffb5911666cce99af6309
View on Chainz β†—

Height

#1,611,372

Difficulty

10.605935

Transactions

1

Size

200 B

Version

2

Bits

0a9b1e88

Nonce

146,218,524

Timestamp

6/2/2016, 7:24:05 PM

Confirmations

5,231,643

Mined by

⛏️ P2SHAc7q4X7ss5sbQcwEyR1PyjwENxtjECe1Pd

Merkle Root

efd2c9dd715326d2a71804bcba104769fad0f9738c4223f7ecff7dd4a087b0ab
Transactions (1)
Coinbaseefd2c9dd715326…ff7dd4a087b0ab
1 in β†’ 1 out8.8800 XPM109 B
Ac7q4X7s…tjECe1Pd
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.

6.893 Γ— 10⁹⁢(97-digit number)
68931292230363323727…49114689783687587841
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
6.893 Γ— 10⁹⁢(97-digit number)
68931292230363323727…49114689783687587841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.378 Γ— 10⁹⁷(98-digit number)
13786258446072664745…98229379567375175681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.757 Γ— 10⁹⁷(98-digit number)
27572516892145329491…96458759134750351361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.514 Γ— 10⁹⁷(98-digit number)
55145033784290658982…92917518269500702721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.102 Γ— 10⁹⁸(99-digit number)
11029006756858131796…85835036539001405441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.205 Γ— 10⁹⁸(99-digit number)
22058013513716263592…71670073078002810881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.411 Γ— 10⁹⁸(99-digit number)
44116027027432527185…43340146156005621761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.823 Γ— 10⁹⁸(99-digit number)
88232054054865054371…86680292312011243521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.764 Γ— 10⁹⁹(100-digit number)
17646410810973010874…73360584624022487041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.529 Γ— 10⁹⁹(100-digit number)
35292821621946021748…46721169248044974081
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:57,988,475 XPMΒ·at block #6,843,014 Β· updates every 60s
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