Block #952,730

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/26/2015, 8:41:10 AM · Difficulty 10.8940 · 5,856,270 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
81021778212b0abea12188e87193d3056d78c96d7a1a3f5d1de76687787c4c02

Height

#952,730

Difficulty

10.894024

Transactions

2

Size

1.14 KB

Version

2

Bits

0ae4debf

Nonce

378,180,264

Timestamp

2/26/2015, 8:41:10 AM

Confirmations

5,856,270

Merkle Root

3155562513eb583c84d735160a215015a9f953e7638c309637e4518ebd68c291
Transactions (2)
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.

1.849 × 10⁹⁶(97-digit number)
18496896364678196505…40256619538470392319
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
1.849 × 10⁹⁶(97-digit number)
18496896364678196505…40256619538470392319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.699 × 10⁹⁶(97-digit number)
36993792729356393010…80513239076940784639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.398 × 10⁹⁶(97-digit number)
73987585458712786021…61026478153881569279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.479 × 10⁹⁷(98-digit number)
14797517091742557204…22052956307763138559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.959 × 10⁹⁷(98-digit number)
29595034183485114408…44105912615526277119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.919 × 10⁹⁷(98-digit number)
59190068366970228817…88211825231052554239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.183 × 10⁹⁸(99-digit number)
11838013673394045763…76423650462105108479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.367 × 10⁹⁸(99-digit number)
23676027346788091526…52847300924210216959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.735 × 10⁹⁸(99-digit number)
47352054693576183053…05694601848420433919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.470 × 10⁹⁸(99-digit number)
94704109387152366107…11389203696840867839
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:57,716,060 XPM·at block #6,808,999 · updates every 60s
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