Block #1,404,692

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/8/2016, 4:48:27 PM · Difficulty 10.8062 · 5,413,319 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8cf2b61015fa15eacda2e02bf934ec95fb00af007a72baef073d65488fb730bf

Height

#1,404,692

Difficulty

10.806249

Transactions

2

Size

1.14 KB

Version

2

Bits

0ace6656

Nonce

616,132,532

Timestamp

1/8/2016, 4:48:27 PM

Confirmations

5,413,319

Merkle Root

ca04e4fc3de6029ba13f99a01edc590ff0d9ce95fe7ebe15442744fc34f9bb5e
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.

1.333 × 10⁹⁶(97-digit number)
13339291853665623321…59055498911593427199
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
1.333 × 10⁹⁶(97-digit number)
13339291853665623321…59055498911593427199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.667 × 10⁹⁶(97-digit number)
26678583707331246642…18110997823186854399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.335 × 10⁹⁶(97-digit number)
53357167414662493284…36221995646373708799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.067 × 10⁹⁷(98-digit number)
10671433482932498656…72443991292747417599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.134 × 10⁹⁷(98-digit number)
21342866965864997313…44887982585494835199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.268 × 10⁹⁷(98-digit number)
42685733931729994627…89775965170989670399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.537 × 10⁹⁷(98-digit number)
85371467863459989255…79551930341979340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.707 × 10⁹⁸(99-digit number)
17074293572691997851…59103860683958681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.414 × 10⁹⁸(99-digit number)
34148587145383995702…18207721367917363199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.829 × 10⁹⁸(99-digit number)
68297174290767991404…36415442735834726399
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:57,788,154 XPM·at block #6,818,010 · updates every 60s
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