Block #1,427,942

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2016, 8:03:16 PM · Difficulty 10.7436 · 5,416,098 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e771a9afc643e938909ed005ad91d4627e09a21d5d02e43de4b89a5c207f157

Height

#1,427,942

Difficulty

10.743561

Transactions

2

Size

866 B

Version

2

Bits

0abe5a08

Nonce

1,133,388,340

Timestamp

1/25/2016, 8:03:16 PM

Confirmations

5,416,098

Merkle Root

1aee5f1bc9315c8deeb3d84a5db45f07c2838376afbeed76d4368b685a80b2f5
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.

1.935 × 10⁹⁵(96-digit number)
19358087074056237892…35423551274324602081
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
1.935 × 10⁹⁵(96-digit number)
19358087074056237892…35423551274324602081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.871 × 10⁹⁵(96-digit number)
38716174148112475785…70847102548649204161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.743 × 10⁹⁵(96-digit number)
77432348296224951571…41694205097298408321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.548 × 10⁹⁶(97-digit number)
15486469659244990314…83388410194596816641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.097 × 10⁹⁶(97-digit number)
30972939318489980628…66776820389193633281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.194 × 10⁹⁶(97-digit number)
61945878636979961257…33553640778387266561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.238 × 10⁹⁷(98-digit number)
12389175727395992251…67107281556774533121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.477 × 10⁹⁷(98-digit number)
24778351454791984502…34214563113549066241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.955 × 10⁹⁷(98-digit number)
49556702909583969005…68429126227098132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.911 × 10⁹⁷(98-digit number)
99113405819167938011…36858252454196264961
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:57,996,689 XPM·at block #6,844,039 · updates every 60s
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