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Block #156,418

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 10:50:22 PM Β· Difficulty 9.8684 Β· 6,670,934 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2e9c9235ce7252bf341f6d8b00201da9e389359dabb22c0261737cacfd268c8d
View on Chainz β†—

Height

#156,418

Difficulty

9.868351

Transactions

1

Size

197 B

Version

2

Bits

09de4c3d

Nonce

22,611

Timestamp

9/8/2013, 10:50:22 PM

Confirmations

6,670,934

Mined by

⛏️ P2SHAW5bQGPKbBrq8V1mi9vfj96pi2goiqzYWr

Merkle Root

226068640555a2b53d8d548bffd1abec963d3057d8c335020608eb9e3184f5ec
Transactions (1)
Coinbase226068640555a2…08eb9e3184f5ec
1 in β†’ 1 out10.2500 XPM109 B
AW5bQGPK…goiqzYWr
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.

2.735 Γ— 10⁹⁰(91-digit number)
27357946981417201529…49329520707185411561
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
2.735 Γ— 10⁹⁰(91-digit number)
27357946981417201529…49329520707185411561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.471 Γ— 10⁹⁰(91-digit number)
54715893962834403059…98659041414370823121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.094 Γ— 10⁹¹(92-digit number)
10943178792566880611…97318082828741646241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.188 Γ— 10⁹¹(92-digit number)
21886357585133761223…94636165657483292481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.377 Γ— 10⁹¹(92-digit number)
43772715170267522447…89272331314966584961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.754 Γ— 10⁹¹(92-digit number)
87545430340535044895…78544662629933169921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.750 Γ— 10⁹²(93-digit number)
17509086068107008979…57089325259866339841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.501 Γ— 10⁹²(93-digit number)
35018172136214017958…14178650519732679681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.003 Γ— 10⁹²(93-digit number)
70036344272428035916…28357301039465359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.400 Γ— 10⁹³(94-digit number)
14007268854485607183…56714602078930718721
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:57,862,915 XPMΒ·at block #6,827,351 Β· updates every 60s
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