Block #915,401

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/30/2015, 2:40:34 AM · Difficulty 10.9262 · 5,900,634 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0018fb34a7443569025f48cf237910f1a705b6dd3ea85a60885f1657ea8f7f51

Height

#915,401

Difficulty

10.926170

Transactions

2

Size

427 B

Version

2

Bits

0aed1979

Nonce

1,325,513,116

Timestamp

1/30/2015, 2:40:34 AM

Confirmations

5,900,634

Merkle Root

911ebe84350ac58ded347cb455ee17b15c3955e2a29d5336de58b9d8be3eacbb
Transactions (2)
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.

1.291 × 10⁹⁴(95-digit number)
12918498938372240739…57617853389376109601
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
1.291 × 10⁹⁴(95-digit number)
12918498938372240739…57617853389376109601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.583 × 10⁹⁴(95-digit number)
25836997876744481478…15235706778752219201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.167 × 10⁹⁴(95-digit number)
51673995753488962956…30471413557504438401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.033 × 10⁹⁵(96-digit number)
10334799150697792591…60942827115008876801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.066 × 10⁹⁵(96-digit number)
20669598301395585182…21885654230017753601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.133 × 10⁹⁵(96-digit number)
41339196602791170365…43771308460035507201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.267 × 10⁹⁵(96-digit number)
82678393205582340730…87542616920071014401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.653 × 10⁹⁶(97-digit number)
16535678641116468146…75085233840142028801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.307 × 10⁹⁶(97-digit number)
33071357282232936292…50170467680284057601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.614 × 10⁹⁶(97-digit number)
66142714564465872584…00340935360568115201
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:57,772,394 XPM·at block #6,816,034 · updates every 60s
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