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Block #155,056

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/8/2013, 2:03:36 AM Β· Difficulty 9.8652 Β· 6,660,915 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
58d089d9913e4c154a566c4a05d841954636a9d63b44f0c3a2a46c7de3590180
View on Chainz β†—

Height

#155,056

Difficulty

9.865227

Transactions

1

Size

197 B

Version

2

Bits

09dd7f83

Nonce

294,507

Timestamp

9/8/2013, 2:03:36 AM

Confirmations

6,660,915

Mined by

⛏️ P2SHATr36r6GPrDWuY8aErt6RmRFsBKgmGvw5f

Merkle Root

e849fcb324a0368d6ef6bca053489691171e683a5d0d76366aa2b8e891d82b15
Transactions (1)
Coinbasee849fcb324a036…a2b8e891d82b15
1 in β†’ 1 out10.2600 XPM109 B
ATr36r6G…KgmGvw5f
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.

2.094 Γ— 10⁹⁰(91-digit number)
20944025545435259584…62413314467768525551
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
2.094 Γ— 10⁹⁰(91-digit number)
20944025545435259584…62413314467768525551
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.188 Γ— 10⁹⁰(91-digit number)
41888051090870519168…24826628935537051101
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.377 Γ— 10⁹⁰(91-digit number)
83776102181741038336…49653257871074102201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.675 Γ— 10⁹¹(92-digit number)
16755220436348207667…99306515742148204401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.351 Γ— 10⁹¹(92-digit number)
33510440872696415334…98613031484296408801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.702 Γ— 10⁹¹(92-digit number)
67020881745392830669…97226062968592817601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.340 Γ— 10⁹²(93-digit number)
13404176349078566133…94452125937185635201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.680 Γ— 10⁹²(93-digit number)
26808352698157132267…88904251874371270401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.361 Γ— 10⁹²(93-digit number)
53616705396314264535…77808503748742540801
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
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