Block #922,273

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 8:28:21 AM · Difficulty 10.9158 · 5,880,258 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
391a6dfb293116f5e2ed19e22dacf69b8ca6a19e4744f4c893712bfbcde4f3d7

Height

#922,273

Difficulty

10.915833

Transactions

5

Size

115.99 KB

Version

2

Bits

0aea7408

Nonce

1,059,188,235

Timestamp

2/4/2015, 8:28:21 AM

Confirmations

5,880,258

Merkle Root

cbbee0db51cc7496d8a08eca520370891881f9cdc284e5af24dddf31f6acf3ba
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out1152.8018 XPM28.95 KB
200 in → 1 out1150.2446 XPM28.94 KB
200 in → 1 out1068.1094 XPM28.94 KB
200 in → 1 out979.0110 XPM28.94 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.

3.416 × 10⁹⁵(96-digit number)
34167256650264948026…53615603780161525761
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
3.416 × 10⁹⁵(96-digit number)
34167256650264948026…53615603780161525761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.833 × 10⁹⁵(96-digit number)
68334513300529896052…07231207560323051521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.366 × 10⁹⁶(97-digit number)
13666902660105979210…14462415120646103041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.733 × 10⁹⁶(97-digit number)
27333805320211958420…28924830241292206081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.466 × 10⁹⁶(97-digit number)
54667610640423916841…57849660482584412161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.093 × 10⁹⁷(98-digit number)
10933522128084783368…15699320965168824321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.186 × 10⁹⁷(98-digit number)
21867044256169566736…31398641930337648641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.373 × 10⁹⁷(98-digit number)
43734088512339133473…62797283860675297281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.746 × 10⁹⁷(98-digit number)
87468177024678266946…25594567721350594561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.749 × 10⁹⁸(99-digit number)
17493635404935653389…51189135442701189121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.498 × 10⁹⁸(99-digit number)
34987270809871306778…02378270885402378241
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:57,664,257 XPM·at block #6,802,530 · updates every 60s
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