Block #708,887

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/6/2014, 12:54:20 AM · Difficulty 10.9570 · 6,101,026 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ee42c4b6612fee5c2b59f63a7dd86200bfcbb2da700b45d04717eddd90836665

Height

#708,887

Difficulty

10.957032

Transactions

2

Size

3.17 KB

Version

2

Bits

0af5000f

Nonce

1,508,081,054

Timestamp

9/6/2014, 12:54:20 AM

Confirmations

6,101,026

Merkle Root

59e8063235aeef857ad6440a3860c8a5fbc146414e821a47c29c1ca4e8cd8beb
Transactions (2)
1 in → 1 out8.5300 XPM116 B
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.

5.755 × 10⁹⁵(96-digit number)
57551690148405371308…73565473034096508321
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
5.755 × 10⁹⁵(96-digit number)
57551690148405371308…73565473034096508321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.151 × 10⁹⁶(97-digit number)
11510338029681074261…47130946068193016641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.302 × 10⁹⁶(97-digit number)
23020676059362148523…94261892136386033281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.604 × 10⁹⁶(97-digit number)
46041352118724297047…88523784272772066561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.208 × 10⁹⁶(97-digit number)
92082704237448594094…77047568545544133121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.841 × 10⁹⁷(98-digit number)
18416540847489718818…54095137091088266241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.683 × 10⁹⁷(98-digit number)
36833081694979437637…08190274182176532481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.366 × 10⁹⁷(98-digit number)
73666163389958875275…16380548364353064961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.473 × 10⁹⁸(99-digit number)
14733232677991775055…32761096728706129921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.946 × 10⁹⁸(99-digit number)
29466465355983550110…65522193457412259841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.893 × 10⁹⁸(99-digit number)
58932930711967100220…31044386914824519681
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:57,723,388 XPM·at block #6,809,912 · updates every 60s
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