Block #942,353

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/18/2015, 9:36:51 PM · Difficulty 10.9012 · 5,884,641 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
23e103e7246a2b1bc611ca53126343ec0586bad812c33c07098b3c855652f06d

Height

#942,353

Difficulty

10.901179

Transactions

6

Size

2.61 KB

Version

2

Bits

0ae6b3ac

Nonce

1,253,252,007

Timestamp

2/18/2015, 9:36:51 PM

Confirmations

5,884,641

Merkle Root

761b0028ef2d885b97f86ee3d7fc42d0b9c84613462ce3d7bd3220077d82251f
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.

3.343 × 10⁹⁶(97-digit number)
33430334291648826033…43409982479814584321
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
3.343 × 10⁹⁶(97-digit number)
33430334291648826033…43409982479814584321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.686 × 10⁹⁶(97-digit number)
66860668583297652067…86819964959629168641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.337 × 10⁹⁷(98-digit number)
13372133716659530413…73639929919258337281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.674 × 10⁹⁷(98-digit number)
26744267433319060826…47279859838516674561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.348 × 10⁹⁷(98-digit number)
53488534866638121653…94559719677033349121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.069 × 10⁹⁸(99-digit number)
10697706973327624330…89119439354066698241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.139 × 10⁹⁸(99-digit number)
21395413946655248661…78238878708133396481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.279 × 10⁹⁸(99-digit number)
42790827893310497322…56477757416266792961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.558 × 10⁹⁸(99-digit number)
85581655786620994645…12955514832533585921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.711 × 10⁹⁹(100-digit number)
17116331157324198929…25911029665067171841
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:57,860,127 XPM·at block #6,826,993 · updates every 60s
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