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Block #1,344,523

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/27/2015, 4:52:41 PM Β· Difficulty 10.8153 Β· 5,497,333 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed024941fea7a27188601b277d7abf217a68457b2afc1525d37397a15ad5ef4c
View on Chainz β†—

Height

#1,344,523

Difficulty

10.815314

Transactions

2

Size

1.28 KB

Version

2

Bits

0ad0b86a

Nonce

1,350,144,130

Timestamp

11/27/2015, 4:52:41 PM

Confirmations

5,497,333

Mined by

⛏️ P2SHALVkq8mn1uNRB9A3zmTgPGwTsCTMsXFFt5

Merkle Root

fcec0d7b7dd58e8d0ac154430fec173d0961e716d23f617289e11add20f936d3
Transactions (2)
Coinbase81418eb2f31d88…638895bcb9aa66
1 in β†’ 1 out8.5600 XPM109 B
ALVkq8mn…TMsXFFt5
07575978b13e87…2db067e2d6baa9
7 in β†’ 2 out5.6726 XPM1.08 KB
AKtCykAm…S9kwqsZ2AbecWDS9…1vtToSML
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.

2.046 Γ— 10⁹⁢(97-digit number)
20466671589302637786…99642918222663699201
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
2.046 Γ— 10⁹⁢(97-digit number)
20466671589302637786…99642918222663699201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.093 Γ— 10⁹⁢(97-digit number)
40933343178605275572…99285836445327398401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.186 Γ— 10⁹⁢(97-digit number)
81866686357210551145…98571672890654796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.637 Γ— 10⁹⁷(98-digit number)
16373337271442110229…97143345781309593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.274 Γ— 10⁹⁷(98-digit number)
32746674542884220458…94286691562619187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.549 Γ— 10⁹⁷(98-digit number)
65493349085768440916…88573383125238374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.309 Γ— 10⁹⁸(99-digit number)
13098669817153688183…77146766250476748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.619 Γ— 10⁹⁸(99-digit number)
26197339634307376366…54293532500953497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.239 Γ— 10⁹⁸(99-digit number)
52394679268614752733…08587065001906995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.047 Γ— 10⁹⁹(100-digit number)
10478935853722950546…17174130003813990401
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:57,979,224 XPMΒ·at block #6,841,855 Β· updates every 60s
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