Block #1,073,961

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 5/24/2015, 5:48:38 PM · Difficulty 10.7416 · 5,753,355 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
29580c55c4b7b4499dca8f2ad8c83b665a0343bcb236ecd2a8e37133ae37dbfa

Height

#1,073,961

Difficulty

10.741600

Transactions

2

Size

869 B

Version

2

Bits

0abdd984

Nonce

167,638,924

Timestamp

5/24/2015, 5:48:38 PM

Confirmations

5,753,355

Merkle Root

4331eb1e7fcf5f900c64aafa22598f61e2e41de68760294d8b339ba9202a07ef
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.

5.991 × 10⁹⁴(95-digit number)
59918691902849666728…83158714149622430801
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
5.991 × 10⁹⁴(95-digit number)
59918691902849666728…83158714149622430801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.198 × 10⁹⁵(96-digit number)
11983738380569933345…66317428299244861601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.396 × 10⁹⁵(96-digit number)
23967476761139866691…32634856598489723201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.793 × 10⁹⁵(96-digit number)
47934953522279733382…65269713196979446401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.586 × 10⁹⁵(96-digit number)
95869907044559466764…30539426393958892801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.917 × 10⁹⁶(97-digit number)
19173981408911893352…61078852787917785601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.834 × 10⁹⁶(97-digit number)
38347962817823786705…22157705575835571201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.669 × 10⁹⁶(97-digit number)
76695925635647573411…44315411151671142401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.533 × 10⁹⁷(98-digit number)
15339185127129514682…88630822303342284801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.067 × 10⁹⁷(98-digit number)
30678370254259029364…77261644606684569601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
6.135 × 10⁹⁷(98-digit number)
61356740508518058729…54523289213369139201
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:57,862,641 XPM·at block #6,827,315 · updates every 60s
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