Block #860,277

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/20/2014, 3:22:58 AM · Difficulty 10.9645 · 5,953,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d919837d9597e895e85ec123302bf021d9e1888364456090f70b1f81ee90d29a

Height

#860,277

Difficulty

10.964493

Transactions

4

Size

1.29 KB

Version

2

Bits

0af6e904

Nonce

543,575,153

Timestamp

12/20/2014, 3:22:58 AM

Confirmations

5,953,935

Merkle Root

6e03a15e2b3aa6bf8b77cb8faea5c2e489efb3eea7233bfc475de7d1a15507c1
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.

5.115 × 10⁹⁴(95-digit number)
51158869245681779823…80846816160468640001
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
5.115 × 10⁹⁴(95-digit number)
51158869245681779823…80846816160468640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.023 × 10⁹⁵(96-digit number)
10231773849136355964…61693632320937280001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.046 × 10⁹⁵(96-digit number)
20463547698272711929…23387264641874560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.092 × 10⁹⁵(96-digit number)
40927095396545423858…46774529283749120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.185 × 10⁹⁵(96-digit number)
81854190793090847716…93549058567498240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.637 × 10⁹⁶(97-digit number)
16370838158618169543…87098117134996480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.274 × 10⁹⁶(97-digit number)
32741676317236339086…74196234269992960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.548 × 10⁹⁶(97-digit number)
65483352634472678173…48392468539985920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.309 × 10⁹⁷(98-digit number)
13096670526894535634…96784937079971840001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.619 × 10⁹⁷(98-digit number)
26193341053789071269…93569874159943680001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.238 × 10⁹⁷(98-digit number)
52386682107578142538…87139748319887360001
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,757,764 XPM·at block #6,814,211 · updates every 60s
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