Block #2,065,580

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2017, 3:13:30 AM · Difficulty 10.8489 · 4,760,970 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
00add3ba654c3e89b0dc4524dbb59b09171f81a8e45e944056983a829f96c8a9

Height

#2,065,580

Difficulty

10.848855

Transactions

2

Size

872 B

Version

2

Bits

0ad94e8e

Nonce

319,885,126

Timestamp

4/11/2017, 3:13:30 AM

Confirmations

4,760,970

Merkle Root

cfaa7320d065a08b9fdaef9066d7cf1e2b6186ada31a1287c3ee83d922b1ed35
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.

5.410 × 10⁹⁶(97-digit number)
54107263947986470430…50146402798321172481
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
5.410 × 10⁹⁶(97-digit number)
54107263947986470430…50146402798321172481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.082 × 10⁹⁷(98-digit number)
10821452789597294086…00292805596642344961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.164 × 10⁹⁷(98-digit number)
21642905579194588172…00585611193284689921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.328 × 10⁹⁷(98-digit number)
43285811158389176344…01171222386569379841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.657 × 10⁹⁷(98-digit number)
86571622316778352689…02342444773138759681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.731 × 10⁹⁸(99-digit number)
17314324463355670537…04684889546277519361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.462 × 10⁹⁸(99-digit number)
34628648926711341075…09369779092555038721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.925 × 10⁹⁸(99-digit number)
69257297853422682151…18739558185110077441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.385 × 10⁹⁹(100-digit number)
13851459570684536430…37479116370220154881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.770 × 10⁹⁹(100-digit number)
27702919141369072860…74958232740440309761
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,856,549 XPM·at block #6,826,549 · updates every 60s
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