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Block #190,435

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2013, 12:01:48 PM Β· Difficulty 9.8738 Β· 6,619,325 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
960685f3a434d8d898bb5d74e067b8ecbcb97d4841595914330849a65c854351
View on Chainz β†—

Height

#190,435

Difficulty

9.873811

Transactions

1

Size

198 B

Version

2

Bits

09dfb210

Nonce

1,848

Timestamp

10/2/2013, 12:01:48 PM

Confirmations

6,619,325

Mined by

⛏️ P2SHAMZkWzWRsMLHogsJNLHamXNwWt28RHPEA5

Merkle Root

c27fe95551865e19166dc7bd308727d1361cad3d0c8cb1e5d1546d7e818fd5e0
Transactions (1)
Coinbasec27fe95551865e…546d7e818fd5e0
1 in β†’ 1 out10.2400 XPM109 B
AMZkWzWR…28RHPEA5
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.

2.622 Γ— 10⁹³(94-digit number)
26228390922368726814…86892347646128413761
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
2.622 Γ— 10⁹³(94-digit number)
26228390922368726814…86892347646128413761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.245 Γ— 10⁹³(94-digit number)
52456781844737453628…73784695292256827521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.049 Γ— 10⁹⁴(95-digit number)
10491356368947490725…47569390584513655041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.098 Γ— 10⁹⁴(95-digit number)
20982712737894981451…95138781169027310081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.196 Γ— 10⁹⁴(95-digit number)
41965425475789962902…90277562338054620161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.393 Γ— 10⁹⁴(95-digit number)
83930850951579925805…80555124676109240321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.678 Γ— 10⁹⁡(96-digit number)
16786170190315985161…61110249352218480641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.357 Γ— 10⁹⁡(96-digit number)
33572340380631970322…22220498704436961281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.714 Γ— 10⁹⁡(96-digit number)
67144680761263940644…44440997408873922561
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:57,722,166 XPMΒ·at block #6,809,759 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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