Block #707,875

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/5/2014, 6:04:51 AM · Difficulty 10.9580 · 6,096,151 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ab2f21da9a90c9d5bb8f69a8f42726d13c5b35f79d58e341d4637b7f94bc5d95

Height

#707,875

Difficulty

10.957987

Transactions

2

Size

650 B

Version

2

Bits

0af53ea3

Nonce

2,489,182,360

Timestamp

9/5/2014, 6:04:51 AM

Confirmations

6,096,151

Merkle Root

3926ba7f41d24f7a96efe400455a00581e2176996d5f9991e94159839117f395
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.

4.323 × 10⁹⁴(95-digit number)
43238376460255616233…99252240089064806719
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
4.323 × 10⁹⁴(95-digit number)
43238376460255616233…99252240089064806719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.647 × 10⁹⁴(95-digit number)
86476752920511232467…98504480178129613439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.729 × 10⁹⁵(96-digit number)
17295350584102246493…97008960356259226879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.459 × 10⁹⁵(96-digit number)
34590701168204492987…94017920712518453759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.918 × 10⁹⁵(96-digit number)
69181402336408985974…88035841425036907519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.383 × 10⁹⁶(97-digit number)
13836280467281797194…76071682850073815039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.767 × 10⁹⁶(97-digit number)
27672560934563594389…52143365700147630079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.534 × 10⁹⁶(97-digit number)
55345121869127188779…04286731400295260159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.106 × 10⁹⁷(98-digit number)
11069024373825437755…08573462800590520319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.213 × 10⁹⁷(98-digit number)
22138048747650875511…17146925601181040639
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,676,259 XPM·at block #6,804,025 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.