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Block #190,454

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/2/2013, 12:16:54 PM Β· Difficulty 9.8739 Β· 6,627,173 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
354fc62676aef0b6001b4d71b3105a9b4e7a325e0148aa49dd9bcdbb8e67a5d0
View on Chainz β†—

Height

#190,454

Difficulty

9.873897

Transactions

1

Size

199 B

Version

2

Bits

09dfb7b4

Nonce

23,705

Timestamp

10/2/2013, 12:16:54 PM

Confirmations

6,627,173

Mined by

⛏️ P2SHAP52EE3FezHothJTJo3Xw2Hi1LZhqfNP3e

Merkle Root

d4bf67ecdeb7712b8cc57cd3ba98415e6b76b1b75f2ad40277a6e4d4fd2439ee
Transactions (1)
Coinbased4bf67ecdeb771…a6e4d4fd2439ee
1 in β†’ 1 out10.2400 XPM109 B
AP52EE3F…ZhqfNP3e
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.

4.273 Γ— 10⁹³(94-digit number)
42739836493321459921…62533073481458016501
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
4.273 Γ— 10⁹³(94-digit number)
42739836493321459921…62533073481458016501
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
8.547 Γ— 10⁹³(94-digit number)
85479672986642919843…25066146962916033001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.709 Γ— 10⁹⁴(95-digit number)
17095934597328583968…50132293925832066001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.419 Γ— 10⁹⁴(95-digit number)
34191869194657167937…00264587851664132001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.838 Γ— 10⁹⁴(95-digit number)
68383738389314335875…00529175703328264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.367 Γ— 10⁹⁡(96-digit number)
13676747677862867175…01058351406656528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.735 Γ— 10⁹⁡(96-digit number)
27353495355725734350…02116702813313056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.470 Γ— 10⁹⁡(96-digit number)
54706990711451468700…04233405626626112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.094 Γ— 10⁹⁢(97-digit number)
10941398142290293740…08466811253252224001
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:57,785,067 XPMΒ·at block #6,817,626 Β· updates every 60s
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