Block #1,160,255

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2015, 5:39:55 PM · Difficulty 10.9387 · 5,666,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd0dfc670618d4c745c056dfbc00e9e3ccdd12b17c5c451de5d807308e186583

Height

#1,160,255

Difficulty

10.938702

Transactions

2

Size

3.74 KB

Version

2

Bits

0af04ec8

Nonce

1,513,980,122

Timestamp

7/18/2015, 5:39:55 PM

Confirmations

5,666,855

Merkle Root

b9773beacb16714a3d3e486b973af481f915d1901f18c68a571151092b44edbc
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.

1.718 × 10⁹²(93-digit number)
17180222534895769089…48260786966636497539
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
1.718 × 10⁹²(93-digit number)
17180222534895769089…48260786966636497539
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.436 × 10⁹²(93-digit number)
34360445069791538178…96521573933272995079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.872 × 10⁹²(93-digit number)
68720890139583076356…93043147866545990159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.374 × 10⁹³(94-digit number)
13744178027916615271…86086295733091980319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.748 × 10⁹³(94-digit number)
27488356055833230542…72172591466183960639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.497 × 10⁹³(94-digit number)
54976712111666461085…44345182932367921279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.099 × 10⁹⁴(95-digit number)
10995342422333292217…88690365864735842559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.199 × 10⁹⁴(95-digit number)
21990684844666584434…77380731729471685119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.398 × 10⁹⁴(95-digit number)
43981369689333168868…54761463458943370239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.796 × 10⁹⁴(95-digit number)
87962739378666337736…09522926917886740479
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:57,861,059 XPM·at block #6,827,109 · updates every 60s
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