Block #922,413

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 11:13:49 AM · Difficulty 10.9154 · 5,884,469 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
32c83fb212f5a30cb76767c24e76ab89710a24c17e1945909fbf10e0d2f53102

Height

#922,413

Difficulty

10.915413

Transactions

5

Size

115.97 KB

Version

2

Bits

0aea5887

Nonce

773,215,714

Timestamp

2/4/2015, 11:13:49 AM

Confirmations

5,884,469

Merkle Root

8f82cad0c8cea2f5d525eb781ebca499c6e2c6f4d23f2c2640edf1f52c940172
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1119.6568 XPM28.95 KB
200 in → 1 out1127.5931 XPM28.93 KB
200 in → 1 out1058.9435 XPM28.94 KB
200 in → 1 out1016.2694 XPM28.94 KB
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.

1.882 × 10⁹⁷(98-digit number)
18827338018769085320…70790291676419263359
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
1.882 × 10⁹⁷(98-digit number)
18827338018769085320…70790291676419263359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.765 × 10⁹⁷(98-digit number)
37654676037538170641…41580583352838526719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.530 × 10⁹⁷(98-digit number)
75309352075076341282…83161166705677053439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.506 × 10⁹⁸(99-digit number)
15061870415015268256…66322333411354106879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.012 × 10⁹⁸(99-digit number)
30123740830030536513…32644666822708213759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.024 × 10⁹⁸(99-digit number)
60247481660061073026…65289333645416427519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.204 × 10⁹⁹(100-digit number)
12049496332012214605…30578667290832855039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.409 × 10⁹⁹(100-digit number)
24098992664024429210…61157334581665710079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.819 × 10⁹⁹(100-digit number)
48197985328048858420…22314669163331420159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.639 × 10⁹⁹(100-digit number)
96395970656097716841…44629338326662840319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.927 × 10¹⁰⁰(101-digit number)
19279194131219543368…89258676653325680639
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:57,699,165 XPM·at block #6,806,881 · updates every 60s
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