Block #2,377,882

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/13/2017, 4:13:31 PM · Difficulty 10.8797 · 4,465,723 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0b3e8384c985f4e5f6799f35e140f2cf8cd62c10d1507aac7d5662315a3c5a1a

Height

#2,377,882

Difficulty

10.879698

Transactions

2

Size

14.01 KB

Version

2

Bits

0ae133df

Nonce

1,847,446,922

Timestamp

11/13/2017, 4:13:31 PM

Confirmations

4,465,723

Merkle Root

57949f631d50a90b71305ea86c8d1f30c22f3b4aa3b030d2cbca2b9460f04f35
Transactions (2)
1 in → 1 out8.5800 XPM109 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.

4.084 × 10⁹⁶(97-digit number)
40847295871013695466…77160443712280985601
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
4.084 × 10⁹⁶(97-digit number)
40847295871013695466…77160443712280985601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.169 × 10⁹⁶(97-digit number)
81694591742027390932…54320887424561971201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.633 × 10⁹⁷(98-digit number)
16338918348405478186…08641774849123942401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.267 × 10⁹⁷(98-digit number)
32677836696810956372…17283549698247884801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.535 × 10⁹⁷(98-digit number)
65355673393621912745…34567099396495769601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.307 × 10⁹⁸(99-digit number)
13071134678724382549…69134198792991539201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.614 × 10⁹⁸(99-digit number)
26142269357448765098…38268397585983078401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.228 × 10⁹⁸(99-digit number)
52284538714897530196…76536795171966156801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.045 × 10⁹⁹(100-digit number)
10456907742979506039…53073590343932313601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.091 × 10⁹⁹(100-digit number)
20913815485959012078…06147180687864627201
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:57,993,204 XPM·at block #6,843,604 · updates every 60s
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