Block #1,692,211

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 7/28/2016, 5:02:43 AM · Difficulty 10.6842 · 5,138,250 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ba7aff73446e91f4cb50e4a61dccfdc2771dde768f8963a5ee71ca6abce12ee0

Height

#1,692,211

Difficulty

10.684241

Transactions

2

Size

868 B

Version

2

Bits

0aaf2a6b

Nonce

217,111,718

Timestamp

7/28/2016, 5:02:43 AM

Confirmations

5,138,250

Merkle Root

d3166728191a215b3c78281a59985f51551d1587367e58cd7a2a6f7de5082c64
Transactions (2)
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.

5.265 × 10⁹⁵(96-digit number)
52651219189221828615…64185420367652908159
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
5.265 × 10⁹⁵(96-digit number)
52651219189221828615…64185420367652908159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.053 × 10⁹⁶(97-digit number)
10530243837844365723…28370840735305816319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.106 × 10⁹⁶(97-digit number)
21060487675688731446…56741681470611632639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.212 × 10⁹⁶(97-digit number)
42120975351377462892…13483362941223265279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.424 × 10⁹⁶(97-digit number)
84241950702754925785…26966725882446530559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.684 × 10⁹⁷(98-digit number)
16848390140550985157…53933451764893061119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.369 × 10⁹⁷(98-digit number)
33696780281101970314…07866903529786122239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.739 × 10⁹⁷(98-digit number)
67393560562203940628…15733807059572244479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.347 × 10⁹⁸(99-digit number)
13478712112440788125…31467614119144488959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.695 × 10⁹⁸(99-digit number)
26957424224881576251…62935228238288977919
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,887,935 XPM·at block #6,830,460 · updates every 60s
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