Block #929,480

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/9/2015, 8:18:00 PM · Difficulty 10.9036 · 5,880,037 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e641a1e85535ad6f852c8ae06c9e004112e0f096fde4d9ff09e3b8366f18bf07

Height

#929,480

Difficulty

10.903571

Transactions

2

Size

366 B

Version

2

Bits

0ae75067

Nonce

2,180,340,007

Timestamp

2/9/2015, 8:18:00 PM

Confirmations

5,880,037

Merkle Root

32272e58359bbadc626e40a057fe4b6f578237c8a49b81befcf6b6d4443f821d
Transactions (2)
1 in → 1 out8.4100 XPM116 B
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.

4.953 × 10⁹⁸(99-digit number)
49531756251392094678…82946934276762112001
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
4.953 × 10⁹⁸(99-digit number)
49531756251392094678…82946934276762112001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
9.906 × 10⁹⁸(99-digit number)
99063512502784189357…65893868553524224001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.981 × 10⁹⁹(100-digit number)
19812702500556837871…31787737107048448001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.962 × 10⁹⁹(100-digit number)
39625405001113675742…63575474214096896001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
7.925 × 10⁹⁹(100-digit number)
79250810002227351485…27150948428193792001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.585 × 10¹⁰⁰(101-digit number)
15850162000445470297…54301896856387584001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.170 × 10¹⁰⁰(101-digit number)
31700324000890940594…08603793712775168001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.340 × 10¹⁰⁰(101-digit number)
63400648001781881188…17207587425550336001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.268 × 10¹⁰¹(102-digit number)
12680129600356376237…34415174851100672001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.536 × 10¹⁰¹(102-digit number)
25360259200712752475…68830349702201344001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.072 × 10¹⁰¹(102-digit number)
50720518401425504950…37660699404402688001
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:57,720,212 XPM·at block #6,809,516 · updates every 60s
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