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Block #136,076

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2013, 12:16:15 AM Β· Difficulty 9.8142 Β· 6,680,265 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6f5256074c8732567fbfc5e62c4c85b46044cac9c8b99061aae362d2f51dfbe9
View on Chainz β†—

Height

#136,076

Difficulty

9.814158

Transactions

1

Size

197 B

Version

2

Bits

09d06ca3

Nonce

73,398

Timestamp

8/27/2013, 12:16:15 AM

Confirmations

6,680,265

Mined by

⛏️ P2SHAY88KHSTJpyaPqTYGEt3LWdPpt88L8yacq

Merkle Root

01258d10651a6d1fbacc74be0721558d6c0f6dea823fd3ecd7fb1f066152e238
Transactions (1)
Coinbase01258d10651a6d…fb1f066152e238
1 in β†’ 1 out10.3700 XPM109 B
AY88KHST…88L8yacq
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.

4.470 Γ— 10⁹⁰(91-digit number)
44709829789802662328…32885272132309417519
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
4.470 Γ— 10⁹⁰(91-digit number)
44709829789802662328…32885272132309417519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.941 Γ— 10⁹⁰(91-digit number)
89419659579605324657…65770544264618835039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.788 Γ— 10⁹¹(92-digit number)
17883931915921064931…31541088529237670079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.576 Γ— 10⁹¹(92-digit number)
35767863831842129863…63082177058475340159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.153 Γ— 10⁹¹(92-digit number)
71535727663684259726…26164354116950680319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.430 Γ— 10⁹²(93-digit number)
14307145532736851945…52328708233901360639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.861 Γ— 10⁹²(93-digit number)
28614291065473703890…04657416467802721279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.722 Γ— 10⁹²(93-digit number)
57228582130947407780…09314832935605442559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.144 Γ— 10⁹³(94-digit number)
11445716426189481556…18629665871210885119
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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