Block #901,545

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/19/2015, 4:08:46 PM · Difficulty 10.9412 · 5,909,425 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e5dbc0774e344dce3c1a1e6fffcd5484f716e3f56fc2abfdb3914963fba19bf5

Height

#901,545

Difficulty

10.941201

Transactions

4

Size

2.56 KB

Version

2

Bits

0af0f294

Nonce

896,857,260

Timestamp

1/19/2015, 4:08:46 PM

Confirmations

5,909,425

Merkle Root

5f750f88198c5f76034001dd9aac45b837c8a78e69db102c38951ce30bb461e5
Transactions (4)
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.

9.372 × 10⁹³(94-digit number)
93724237401848010953…85282763496846924971
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
9.372 × 10⁹³(94-digit number)
93724237401848010953…85282763496846924971
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.874 × 10⁹⁴(95-digit number)
18744847480369602190…70565526993693849941
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.748 × 10⁹⁴(95-digit number)
37489694960739204381…41131053987387699881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.497 × 10⁹⁴(95-digit number)
74979389921478408763…82262107974775399761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.499 × 10⁹⁵(96-digit number)
14995877984295681752…64524215949550799521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.999 × 10⁹⁵(96-digit number)
29991755968591363505…29048431899101599041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.998 × 10⁹⁵(96-digit number)
59983511937182727010…58096863798203198081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.199 × 10⁹⁶(97-digit number)
11996702387436545402…16193727596406396161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.399 × 10⁹⁶(97-digit number)
23993404774873090804…32387455192812792321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.798 × 10⁹⁶(97-digit number)
47986809549746181608…64774910385625584641
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:57,731,862 XPM·at block #6,810,969 · updates every 60s
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