Block #954,111

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/27/2015, 8:56:10 AM · Difficulty 10.8925 · 5,856,563 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
200c4bfcc19273911f10a8ddfd6aa7b44617fd3b34639023313055f8578490cf

Height

#954,111

Difficulty

10.892522

Transactions

4

Size

13.73 KB

Version

2

Bits

0ae47c5a

Nonce

643,320,212

Timestamp

2/27/2015, 8:56:10 AM

Confirmations

5,856,563

Merkle Root

59843815a4643d5fa464f596ee8bc05f0d455e284b4fbb299c588eee3f006889
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.

1.450 × 10⁹⁷(98-digit number)
14504587802221139925…99866586226949079039
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
1.450 × 10⁹⁷(98-digit number)
14504587802221139925…99866586226949079039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.900 × 10⁹⁷(98-digit number)
29009175604442279851…99733172453898158079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.801 × 10⁹⁷(98-digit number)
58018351208884559703…99466344907796316159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.160 × 10⁹⁸(99-digit number)
11603670241776911940…98932689815592632319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.320 × 10⁹⁸(99-digit number)
23207340483553823881…97865379631185264639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.641 × 10⁹⁸(99-digit number)
46414680967107647762…95730759262370529279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.282 × 10⁹⁸(99-digit number)
92829361934215295525…91461518524741058559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.856 × 10⁹⁹(100-digit number)
18565872386843059105…82923037049482117119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.713 × 10⁹⁹(100-digit number)
37131744773686118210…65846074098964234239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.426 × 10⁹⁹(100-digit number)
74263489547372236420…31692148197928468479
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,729,483 XPM·at block #6,810,673 · updates every 60s
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