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Block #69,480

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/20/2013, 9:01:37 AM Β· Difficulty 8.9910 Β· 6,725,520 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
71c84fbc739be86e767e84586060ee79b8fe548ec24caafea7b101e7d8bbf84f
View on Chainz β†—

Height

#69,480

Difficulty

8.990981

Transactions

1

Size

199 B

Version

2

Bits

08fdb0ee

Nonce

52

Timestamp

7/20/2013, 9:01:37 AM

Confirmations

6,725,520

Mined by

⛏️ P2SHAXSFye4rUycSu1xJ6pmwUfhCbvADf1YWCU

Merkle Root

3d526c8607337f30f18d403441d5f21b7f0ce1d387a12cce57379a1d3bc7c8e7
Transactions (1)
Coinbase3d526c8607337f…379a1d3bc7c8e7
1 in β†’ 1 out12.3500 XPM110 B
AXSFye4r…ADf1YWCU
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.

1.123 Γ— 10⁹³(94-digit number)
11237838978501323973…37592972832313169919
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
1.123 Γ— 10⁹³(94-digit number)
11237838978501323973…37592972832313169919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.247 Γ— 10⁹³(94-digit number)
22475677957002647947…75185945664626339839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.495 Γ— 10⁹³(94-digit number)
44951355914005295895…50371891329252679679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.990 Γ— 10⁹³(94-digit number)
89902711828010591791…00743782658505359359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.798 Γ— 10⁹⁴(95-digit number)
17980542365602118358…01487565317010718719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.596 Γ— 10⁹⁴(95-digit number)
35961084731204236716…02975130634021437439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.192 Γ— 10⁹⁴(95-digit number)
71922169462408473433…05950261268042874879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.438 Γ— 10⁹⁡(96-digit number)
14384433892481694686…11900522536085749759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.876 Γ— 10⁹⁡(96-digit number)
28768867784963389373…23801045072171499519
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
Circulating Supply:57,604,043 XPMΒ·at block #6,794,999 Β· updates every 60s
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