Block #922,429

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 11:35:16 AM · Difficulty 10.9154 · 5,873,111 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7324147ba0d9612ab76013599530dfcc680aad94c7046a5f0b4b9f9a4b5b7f0e

Height

#922,429

Difficulty

10.915352

Transactions

5

Size

116.02 KB

Version

2

Bits

0aea5482

Nonce

190,085,049

Timestamp

2/4/2015, 11:35:16 AM

Confirmations

5,873,111

Merkle Root

61eed1d719ba012f760a75b0333801087ac3d68cd830592edb3b1ff9d208e4e5
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1038.8358 XPM28.96 KB
200 in → 1 out1006.4441 XPM28.95 KB
200 in → 1 out1052.5363 XPM28.95 KB
200 in → 1 out983.6669 XPM28.95 KB
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.

3.721 × 10⁹⁵(96-digit number)
37217320907505936027…61806683601613799121
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
3.721 × 10⁹⁵(96-digit number)
37217320907505936027…61806683601613799121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.443 × 10⁹⁵(96-digit number)
74434641815011872055…23613367203227598241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.488 × 10⁹⁶(97-digit number)
14886928363002374411…47226734406455196481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.977 × 10⁹⁶(97-digit number)
29773856726004748822…94453468812910392961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.954 × 10⁹⁶(97-digit number)
59547713452009497644…88906937625820785921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.190 × 10⁹⁷(98-digit number)
11909542690401899528…77813875251641571841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.381 × 10⁹⁷(98-digit number)
23819085380803799057…55627750503283143681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.763 × 10⁹⁷(98-digit number)
47638170761607598115…11255501006566287361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.527 × 10⁹⁷(98-digit number)
95276341523215196230…22511002013132574721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.905 × 10⁹⁸(99-digit number)
19055268304643039246…45022004026265149441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.811 × 10⁹⁸(99-digit number)
38110536609286078492…90044008052530298881
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:57,608,385 XPM·at block #6,795,539 · updates every 60s
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