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Block #192,600

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/3/2013, 11:47:46 PM Β· Difficulty 9.8746 Β· 6,611,595 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0ba5ba56abc430b46243f8ebfedf58ef4ae8856e071b33e41dcf3f09bc93ee3d
View on Chainz β†—

Height

#192,600

Difficulty

9.874577

Transactions

1

Size

198 B

Version

2

Bits

09dfe44f

Nonce

370,771

Timestamp

10/3/2013, 11:47:46 PM

Confirmations

6,611,595

Mined by

⛏️ P2SHAQ4KuZ2UkkCs8rHce3kHkL7Wmf1UKD59gi

Merkle Root

e41bc1c33a1d1b9681169de8cadd5aca0be0d7d7128dfa816bbd3643fa670b6c
Transactions (1)
Coinbasee41bc1c33a1d1b…bd3643fa670b6c
1 in β†’ 1 out10.2400 XPM109 B
AQ4KuZ2U…1UKD59gi
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.

1.754 Γ— 10⁹²(93-digit number)
17547306196924607074…54768375307847990561
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
1.754 Γ— 10⁹²(93-digit number)
17547306196924607074…54768375307847990561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.509 Γ— 10⁹²(93-digit number)
35094612393849214148…09536750615695981121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.018 Γ— 10⁹²(93-digit number)
70189224787698428296…19073501231391962241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.403 Γ— 10⁹³(94-digit number)
14037844957539685659…38147002462783924481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.807 Γ— 10⁹³(94-digit number)
28075689915079371318…76294004925567848961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.615 Γ— 10⁹³(94-digit number)
56151379830158742636…52588009851135697921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.123 Γ— 10⁹⁴(95-digit number)
11230275966031748527…05176019702271395841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.246 Γ— 10⁹⁴(95-digit number)
22460551932063497054…10352039404542791681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.492 Γ— 10⁹⁴(95-digit number)
44921103864126994109…20704078809085583361
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:57,677,614 XPMΒ·at block #6,804,194 Β· updates every 60s
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