Block #1,119,851

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/20/2015, 9:16:31 PM · Difficulty 10.9336 · 5,696,170 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
857178671c00d374bddb19a20afec4b3d22081bcd44052748bebac7ee9a3cd07

Height

#1,119,851

Difficulty

10.933594

Transactions

2

Size

426 B

Version

2

Bits

0aeefffd

Nonce

228,003,713

Timestamp

6/20/2015, 9:16:31 PM

Confirmations

5,696,170

Merkle Root

3b5e0411d3051b8044af3927f402716cfc41780277aee7b94a31efb2c174d7b3
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.

2.733 × 10⁹¹(92-digit number)
27330408533966225281…93936515590197343101
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
2.733 × 10⁹¹(92-digit number)
27330408533966225281…93936515590197343101
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.466 × 10⁹¹(92-digit number)
54660817067932450563…87873031180394686201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.093 × 10⁹²(93-digit number)
10932163413586490112…75746062360789372401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.186 × 10⁹²(93-digit number)
21864326827172980225…51492124721578744801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.372 × 10⁹²(93-digit number)
43728653654345960451…02984249443157489601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.745 × 10⁹²(93-digit number)
87457307308691920902…05968498886314979201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.749 × 10⁹³(94-digit number)
17491461461738384180…11936997772629958401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.498 × 10⁹³(94-digit number)
34982922923476768360…23873995545259916801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.996 × 10⁹³(94-digit number)
69965845846953536721…47747991090519833601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.399 × 10⁹⁴(95-digit number)
13993169169390707344…95495982181039667201
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:57,772,280 XPM·at block #6,816,020 · updates every 60s
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