Block #377,194

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/26/2014, 10:44:00 PM · Difficulty 10.4239 · 6,433,396 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
672efb80a76930cf31680e3851c54eefde708a9ed4c362851ab9227db7fd79bc

Height

#377,194

Difficulty

10.423875

Transactions

5

Size

1.09 KB

Version

2

Bits

0a6c830c

Nonce

389

Timestamp

1/26/2014, 10:44:00 PM

Confirmations

6,433,396

Merkle Root

44d72e5b427d96d4da0833470b278c699f9b6abb5252af00c76529b0816c4495
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.

1.358 × 10¹⁰¹(102-digit number)
13580658671615834772…88073504645698027521
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
1.358 × 10¹⁰¹(102-digit number)
13580658671615834772…88073504645698027521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.716 × 10¹⁰¹(102-digit number)
27161317343231669545…76147009291396055041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.432 × 10¹⁰¹(102-digit number)
54322634686463339090…52294018582792110081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.086 × 10¹⁰²(103-digit number)
10864526937292667818…04588037165584220161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.172 × 10¹⁰²(103-digit number)
21729053874585335636…09176074331168440321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.345 × 10¹⁰²(103-digit number)
43458107749170671272…18352148662336880641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.691 × 10¹⁰²(103-digit number)
86916215498341342544…36704297324673761281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.738 × 10¹⁰³(104-digit number)
17383243099668268508…73408594649347522561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.476 × 10¹⁰³(104-digit number)
34766486199336537017…46817189298695045121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.953 × 10¹⁰³(104-digit number)
69532972398673074035…93634378597390090241
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:57,728,806 XPM·at block #6,810,589 · updates every 60s
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