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Block #191,269

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/3/2013, 12:37:20 AM Β· Difficulty 9.8759 Β· 6,625,648 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ba91b517b7b268d7ea2c6e836e595259bd335a5501e0241e2af9bc93bdb8bd04
View on Chainz β†—

Height

#191,269

Difficulty

9.875855

Transactions

2

Size

470 B

Version

2

Bits

09e0380c

Nonce

540,042

Timestamp

10/3/2013, 12:37:20 AM

Confirmations

6,625,648

Mined by

⛏️ P2SHASHCgr3FcMvAMVeUbxmte178wGe7VPFbY8

Merkle Root

fd22b0c06a4e4451fdc3c4f010464e2c8897e40c747963375efc4030d8aa78f6
Transactions (2)
Coinbase34995feff6cd53…775964ea04d0de
1 in β†’ 1 out10.2500 XPM109 B
ASHCgr3F…e7VPFbY8
caeae039fcf656…94dabf483f50b9
2 in β†’ 1 out20.8400 XPM271 B
AYeqnQ3n…eec9bEMp
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.

2.024 Γ— 10⁹⁡(96-digit number)
20242513127144696346…34439329766745274881
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
2.024 Γ— 10⁹⁡(96-digit number)
20242513127144696346…34439329766745274881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.048 Γ— 10⁹⁡(96-digit number)
40485026254289392692…68878659533490549761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.097 Γ— 10⁹⁡(96-digit number)
80970052508578785385…37757319066981099521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.619 Γ— 10⁹⁢(97-digit number)
16194010501715757077…75514638133962199041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.238 Γ— 10⁹⁢(97-digit number)
32388021003431514154…51029276267924398081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.477 Γ— 10⁹⁢(97-digit number)
64776042006863028308…02058552535848796161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.295 Γ— 10⁹⁷(98-digit number)
12955208401372605661…04117105071697592321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.591 Γ— 10⁹⁷(98-digit number)
25910416802745211323…08234210143395184641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.182 Γ— 10⁹⁷(98-digit number)
51820833605490422646…16468420286790369281
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,779,377 XPMΒ·at block #6,816,916 Β· updates every 60s
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