Block #379,793

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2014, 6:39:36 PM · Difficulty 10.4199 · 6,434,419 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9625de042cdde61af2ccfcc75a88e0ba2a471f3485c9be0cb44fe91f708adc56

Height

#379,793

Difficulty

10.419874

Transactions

5

Size

1.23 KB

Version

2

Bits

0a6b7cd8

Nonce

95,458

Timestamp

1/28/2014, 6:39:36 PM

Confirmations

6,434,419

Merkle Root

e60b232baa117685900c1b60e2fd409dd37879911a948017ee96de2fdd976d52
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.

1.941 × 10⁹⁴(95-digit number)
19412879845597321254…57475814863373071361
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
1.941 × 10⁹⁴(95-digit number)
19412879845597321254…57475814863373071361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.882 × 10⁹⁴(95-digit number)
38825759691194642509…14951629726746142721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.765 × 10⁹⁴(95-digit number)
77651519382389285019…29903259453492285441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.553 × 10⁹⁵(96-digit number)
15530303876477857003…59806518906984570881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.106 × 10⁹⁵(96-digit number)
31060607752955714007…19613037813969141761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.212 × 10⁹⁵(96-digit number)
62121215505911428015…39226075627938283521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.242 × 10⁹⁶(97-digit number)
12424243101182285603…78452151255876567041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.484 × 10⁹⁶(97-digit number)
24848486202364571206…56904302511753134081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.969 × 10⁹⁶(97-digit number)
49696972404729142412…13808605023506268161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.939 × 10⁹⁶(97-digit number)
99393944809458284824…27617210047012536321
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:57,757,764 XPM·at block #6,814,211 · updates every 60s
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