Block #907,308

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/24/2015, 12:43:12 AM · Difficulty 10.9351 · 5,898,952 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
41e2c167840f2164615078fc60738b4130dff0f25dcc54c575e51c86a664e2af

Height

#907,308

Difficulty

10.935060

Transactions

3

Size

659 B

Version

2

Bits

0aef601f

Nonce

696,489,615

Timestamp

1/24/2015, 12:43:12 AM

Confirmations

5,898,952

Merkle Root

018734b93a8e3b4e2c120a7789021bc4f4605395d9cc64ffb869b525c8a5e7e6
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.

3.482 × 10⁹⁴(95-digit number)
34823425469429431050…74680781340703790401
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
3.482 × 10⁹⁴(95-digit number)
34823425469429431050…74680781340703790401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.964 × 10⁹⁴(95-digit number)
69646850938858862100…49361562681407580801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.392 × 10⁹⁵(96-digit number)
13929370187771772420…98723125362815161601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.785 × 10⁹⁵(96-digit number)
27858740375543544840…97446250725630323201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.571 × 10⁹⁵(96-digit number)
55717480751087089680…94892501451260646401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.114 × 10⁹⁶(97-digit number)
11143496150217417936…89785002902521292801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.228 × 10⁹⁶(97-digit number)
22286992300434835872…79570005805042585601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.457 × 10⁹⁶(97-digit number)
44573984600869671744…59140011610085171201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.914 × 10⁹⁶(97-digit number)
89147969201739343489…18280023220170342401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.782 × 10⁹⁷(98-digit number)
17829593840347868697…36560046440340684801
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:57,694,164 XPM·at block #6,806,259 · updates every 60s
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