Block #911,325

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/27/2015, 12:35:09 AM · Difficulty 10.9313 · 5,893,748 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
44d7c79ba99dcfe22188484205065a739440358151a874826a38eb4abbe1fac7

Height

#911,325

Difficulty

10.931281

Transactions

2

Size

1.72 KB

Version

2

Bits

0aee6868

Nonce

995,114,560

Timestamp

1/27/2015, 12:35:09 AM

Confirmations

5,893,748

Merkle Root

074bbab2b93cbf4cf463c0ef0070522d05b86a997986ef740c712dd8ca1aafdb
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.

2.017 × 10⁹⁷(98-digit number)
20176626933863044718…69811606425212897281
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
2.017 × 10⁹⁷(98-digit number)
20176626933863044718…69811606425212897281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.035 × 10⁹⁷(98-digit number)
40353253867726089437…39623212850425794561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.070 × 10⁹⁷(98-digit number)
80706507735452178874…79246425700851589121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.614 × 10⁹⁸(99-digit number)
16141301547090435774…58492851401703178241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.228 × 10⁹⁸(99-digit number)
32282603094180871549…16985702803406356481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.456 × 10⁹⁸(99-digit number)
64565206188361743099…33971405606812712961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.291 × 10⁹⁹(100-digit number)
12913041237672348619…67942811213625425921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.582 × 10⁹⁹(100-digit number)
25826082475344697239…35885622427250851841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.165 × 10⁹⁹(100-digit number)
51652164950689394479…71771244854501703681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.033 × 10¹⁰⁰(101-digit number)
10330432990137878895…43542489709003407361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.066 × 10¹⁰⁰(101-digit number)
20660865980275757791…87084979418006814721
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,684,651 XPM·at block #6,805,072 · updates every 60s
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