Block #602,765

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/26/2014, 1:06:08 PM · Difficulty 10.9129 · 6,207,791 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd9c2015931fe9d55da192e0005bd1bdc301d55ee65c4dab324d922258c45512

Height

#602,765

Difficulty

10.912892

Transactions

2

Size

822 B

Version

2

Bits

0ae9b345

Nonce

194,103

Timestamp

6/26/2014, 1:06:08 PM

Confirmations

6,207,791

Merkle Root

15eea8b9893c80f1c3aa4c2a176951e6b96403929e6c019d012be665c37162a3
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

7.237 × 10⁹³(94-digit number)
72370363816641811849…44433203340976923599
Discovered Prime Numbers
p_k = 2^k × 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
7.237 × 10⁹³(94-digit number)
72370363816641811849…44433203340976923599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.447 × 10⁹⁴(95-digit number)
14474072763328362369…88866406681953847199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.894 × 10⁹⁴(95-digit number)
28948145526656724739…77732813363907694399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.789 × 10⁹⁴(95-digit number)
57896291053313449479…55465626727815388799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.157 × 10⁹⁵(96-digit number)
11579258210662689895…10931253455630777599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.315 × 10⁹⁵(96-digit number)
23158516421325379791…21862506911261555199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.631 × 10⁹⁵(96-digit number)
46317032842650759583…43725013822523110399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.263 × 10⁹⁵(96-digit number)
92634065685301519166…87450027645046220799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.852 × 10⁹⁶(97-digit number)
18526813137060303833…74900055290092441599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.705 × 10⁹⁶(97-digit number)
37053626274120607666…49800110580184883199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
7.410 × 10⁹⁶(97-digit number)
74107252548241215333…99600221160369766399
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,728,537 XPM·at block #6,810,555 · updates every 60s
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