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Block #682,157

1CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the First Kind Β· Discovered 8/18/2014, 1:33:16 AM Β· Difficulty 10.9610 Β· 6,135,464 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c2d8a5a47d7587f9217f562015439d1e7b412b95f9fb7371c8bd8d520b014b7d
View on Chainz β†—

Height

#682,157

Difficulty

10.961019

Transactions

2

Size

1.69 KB

Version

2

Bits

0af60551

Nonce

700,365,568

Timestamp

8/18/2014, 1:33:16 AM

Confirmations

6,135,464

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

63cc6187d2f1b37d682aa299e6adc45b6d388e39b496b4f3659e2d81fcf6b926
Transactions (2)
Coinbase383329e9b9bc7f…0428096bfc8770
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
5c98d591650d4a…29073fdb83993d
10 in β†’ 1 out30.2580 XPM1.49 KB
ASKjXoz1…cFZ41bU7
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.

5.791 Γ— 10⁹⁸(99-digit number)
57915190628077032991…23906196432420399999
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
5.791 Γ— 10⁹⁸(99-digit number)
57915190628077032991…23906196432420399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.158 Γ— 10⁹⁹(100-digit number)
11583038125615406598…47812392864840799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.316 Γ— 10⁹⁹(100-digit number)
23166076251230813196…95624785729681599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.633 Γ— 10⁹⁹(100-digit number)
46332152502461626393…91249571459363199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.266 Γ— 10⁹⁹(100-digit number)
92664305004923252786…82499142918726399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.853 Γ— 10¹⁰⁰(101-digit number)
18532861000984650557…64998285837452799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.706 Γ— 10¹⁰⁰(101-digit number)
37065722001969301114…29996571674905599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.413 Γ— 10¹⁰⁰(101-digit number)
74131444003938602229…59993143349811199999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.482 Γ— 10¹⁰¹(102-digit number)
14826288800787720445…19986286699622399999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.965 Γ— 10¹⁰¹(102-digit number)
29652577601575440891…39972573399244799999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.930 Γ— 10¹⁰¹(102-digit number)
59305155203150881783…79945146798489599999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
1.186 Γ— 10¹⁰²(103-digit number)
11861031040630176356…59890293596979199999
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,785,018 XPMΒ·at block #6,817,620 Β· updates every 60s
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