Block #1,489,740

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2016, 8:05:33 AM · Difficulty 10.6999 · 5,343,594 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b245466390b08a81cf973107587eb7e1ae07522b122d6c0d5ccbbdb49b671c59

Height

#1,489,740

Difficulty

10.699878

Transactions

2

Size

1.22 KB

Version

2

Bits

0ab32b34

Nonce

65,083

Timestamp

3/9/2016, 8:05:33 AM

Confirmations

5,343,594

Merkle Root

66ce60e4ce2e978b0da52221d1335399988837228660d3acbe8de3783828f83d
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.

6.520 × 10¹⁰⁴(105-digit number)
65206184309886696568…45870300743414618401
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
6.520 × 10¹⁰⁴(105-digit number)
65206184309886696568…45870300743414618401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.304 × 10¹⁰⁵(106-digit number)
13041236861977339313…91740601486829236801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.608 × 10¹⁰⁵(106-digit number)
26082473723954678627…83481202973658473601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.216 × 10¹⁰⁵(106-digit number)
52164947447909357255…66962405947316947201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.043 × 10¹⁰⁶(107-digit number)
10432989489581871451…33924811894633894401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.086 × 10¹⁰⁶(107-digit number)
20865978979163742902…67849623789267788801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.173 × 10¹⁰⁶(107-digit number)
41731957958327485804…35699247578535577601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.346 × 10¹⁰⁶(107-digit number)
83463915916654971608…71398495157071155201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.669 × 10¹⁰⁷(108-digit number)
16692783183330994321…42796990314142310401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.338 × 10¹⁰⁷(108-digit number)
33385566366661988643…85593980628284620801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.677 × 10¹⁰⁷(108-digit number)
66771132733323977286…71187961256569241601
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:57,910,867 XPM·at block #6,833,333 · updates every 60s
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