Block #1,125,842

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/25/2015, 5:32:25 AM · Difficulty 10.9302 · 5,688,114 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
061ff63fe7e4b224782d65fc497362bfdb2df919270636f31bfcfc1901e1af73

Height

#1,125,842

Difficulty

10.930182

Transactions

2

Size

2.58 KB

Version

2

Bits

0aee2060

Nonce

1,450,878,975

Timestamp

6/25/2015, 5:32:25 AM

Confirmations

5,688,114

Merkle Root

7e7b32ee74a1520d40155e63eea10ca77cef6292d88e03353c5fe4d54d96c7c1
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.

1.085 × 10⁹⁶(97-digit number)
10850598322948802239…13503277346902190081
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
1.085 × 10⁹⁶(97-digit number)
10850598322948802239…13503277346902190081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.170 × 10⁹⁶(97-digit number)
21701196645897604478…27006554693804380161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.340 × 10⁹⁶(97-digit number)
43402393291795208956…54013109387608760321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.680 × 10⁹⁶(97-digit number)
86804786583590417912…08026218775217520641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.736 × 10⁹⁷(98-digit number)
17360957316718083582…16052437550435041281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.472 × 10⁹⁷(98-digit number)
34721914633436167164…32104875100870082561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.944 × 10⁹⁷(98-digit number)
69443829266872334329…64209750201740165121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.388 × 10⁹⁸(99-digit number)
13888765853374466865…28419500403480330241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.777 × 10⁹⁸(99-digit number)
27777531706748933731…56839000806960660481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.555 × 10⁹⁸(99-digit number)
55555063413497867463…13678001613921320961
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,755,724 XPM·at block #6,813,955 · updates every 60s
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