Block #1,216,798

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/1/2015, 7:26:54 AM · Difficulty 10.7255 · 5,626,436 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d81ab69b8b81f9d8ea24b7f374408d5c45bb86bd76564528774b2b65623b662f

Height

#1,216,798

Difficulty

10.725496

Transactions

3

Size

806 B

Version

2

Bits

0ab9ba17

Nonce

404,074,648

Timestamp

9/1/2015, 7:26:54 AM

Confirmations

5,626,436

Merkle Root

0bd7dc510ce894de6e693b61398d2ed8d405ba08ba2bfc93da3542fc9b4e6885
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.

9.848 × 10⁹⁶(97-digit number)
98481011178691745054…92993395587793058399
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
9.848 × 10⁹⁶(97-digit number)
98481011178691745054…92993395587793058399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.969 × 10⁹⁷(98-digit number)
19696202235738349010…85986791175586116799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.939 × 10⁹⁷(98-digit number)
39392404471476698021…71973582351172233599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.878 × 10⁹⁷(98-digit number)
78784808942953396043…43947164702344467199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.575 × 10⁹⁸(99-digit number)
15756961788590679208…87894329404688934399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.151 × 10⁹⁸(99-digit number)
31513923577181358417…75788658809377868799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.302 × 10⁹⁸(99-digit number)
63027847154362716834…51577317618755737599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.260 × 10⁹⁹(100-digit number)
12605569430872543366…03154635237511475199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.521 × 10⁹⁹(100-digit number)
25211138861745086733…06309270475022950399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.042 × 10⁹⁹(100-digit number)
50422277723490173467…12618540950045900799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.008 × 10¹⁰⁰(101-digit number)
10084455544698034693…25237081900091801599
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,990,247 XPM·at block #6,843,233 · updates every 60s
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