Block #373,277

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2014, 5:01:48 AM · Difficulty 10.4251 · 6,437,044 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d767e2c936c14ad9849944b5d78570059835c10ff87f0be9a88185fa57a912fe

Height

#373,277

Difficulty

10.425085

Transactions

4

Size

814 B

Version

2

Bits

0a6cd260

Nonce

67,112,458

Timestamp

1/24/2014, 5:01:48 AM

Confirmations

6,437,044

Merkle Root

4548f128a271354790e7b72c04f8b66ebb27874d2a2342b5e0b895254eaa204b
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.

6.260 × 10⁹⁴(95-digit number)
62608164244847738672…75889780596211091601
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
6.260 × 10⁹⁴(95-digit number)
62608164244847738672…75889780596211091601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.252 × 10⁹⁵(96-digit number)
12521632848969547734…51779561192422183201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.504 × 10⁹⁵(96-digit number)
25043265697939095469…03559122384844366401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.008 × 10⁹⁵(96-digit number)
50086531395878190938…07118244769688732801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.001 × 10⁹⁶(97-digit number)
10017306279175638187…14236489539377465601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.003 × 10⁹⁶(97-digit number)
20034612558351276375…28472979078754931201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.006 × 10⁹⁶(97-digit number)
40069225116702552750…56945958157509862401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.013 × 10⁹⁶(97-digit number)
80138450233405105501…13891916315019724801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.602 × 10⁹⁷(98-digit number)
16027690046681021100…27783832630039449601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.205 × 10⁹⁷(98-digit number)
32055380093362042200…55567665260078899201
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:57,726,646 XPM·at block #6,810,320 · updates every 60s
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