Block #2,064,928

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2017, 5:23:56 PM · Difficulty 10.8470 · 4,780,049 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eedb26d5c203bca9e09a7f97f43a44c2786887d56f266b02b11790da88a7e81f

Height

#2,064,928

Difficulty

10.846958

Transactions

38

Size

12.20 KB

Version

2

Bits

0ad8d239

Nonce

1,892,959,114

Timestamp

4/10/2017, 5:23:56 PM

Confirmations

4,780,049

Merkle Root

bc53341893af97c886b727afd44ee09f40c043358e0e30e6304b064d0f844968
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.

2.245 × 10⁹⁷(98-digit number)
22450532379493073899…93663498813723258881
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
2.245 × 10⁹⁷(98-digit number)
22450532379493073899…93663498813723258881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.490 × 10⁹⁷(98-digit number)
44901064758986147799…87326997627446517761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.980 × 10⁹⁷(98-digit number)
89802129517972295599…74653995254893035521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.796 × 10⁹⁸(99-digit number)
17960425903594459119…49307990509786071041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.592 × 10⁹⁸(99-digit number)
35920851807188918239…98615981019572142081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.184 × 10⁹⁸(99-digit number)
71841703614377836479…97231962039144284161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.436 × 10⁹⁹(100-digit number)
14368340722875567295…94463924078288568321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.873 × 10⁹⁹(100-digit number)
28736681445751134591…88927848156577136641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.747 × 10⁹⁹(100-digit number)
57473362891502269183…77855696313154273281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.149 × 10¹⁰⁰(101-digit number)
11494672578300453836…55711392626308546561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.298 × 10¹⁰⁰(101-digit number)
22989345156600907673…11422785252617093121
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:58,004,235 XPM·at block #6,844,976 · updates every 60s
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