Block #901,230

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/19/2015, 10:08:08 AM · Difficulty 10.9417 · 5,907,388 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
474cb6e68773d17240cc439b6f335522a275c284d8ad10243700f2929bb41a65

Height

#901,230

Difficulty

10.941680

Transactions

1

Size

243 B

Version

2

Bits

0af111f9

Nonce

35,453,280

Timestamp

1/19/2015, 10:08:08 AM

Confirmations

5,907,388

Merkle Root

2b3e74fa4d73ec6459527597524803707d9ddd7fa37e4723897b32d569cd2173
Transactions (1)
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.

1.071 × 10⁹⁷(98-digit number)
10715379307888283247…85773496454185484801
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
1.071 × 10⁹⁷(98-digit number)
10715379307888283247…85773496454185484801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.143 × 10⁹⁷(98-digit number)
21430758615776566495…71546992908370969601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.286 × 10⁹⁷(98-digit number)
42861517231553132991…43093985816741939201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.572 × 10⁹⁷(98-digit number)
85723034463106265983…86187971633483878401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.714 × 10⁹⁸(99-digit number)
17144606892621253196…72375943266967756801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.428 × 10⁹⁸(99-digit number)
34289213785242506393…44751886533935513601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.857 × 10⁹⁸(99-digit number)
68578427570485012786…89503773067871027201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.371 × 10⁹⁹(100-digit number)
13715685514097002557…79007546135742054401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.743 × 10⁹⁹(100-digit number)
27431371028194005114…58015092271484108801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.486 × 10⁹⁹(100-digit number)
54862742056388010229…16030184542968217601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.097 × 10¹⁰⁰(101-digit number)
10972548411277602045…32060369085936435201
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:57,712,994 XPM·at block #6,808,617 · updates every 60s
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