Block #1,369,152

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 12/14/2015, 3:08:34 PM · Difficulty 10.8256 · 5,457,564 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2efe198ae77b03b7560aab523e1fb176651e17a690090bb8d386c6a2a009733e

Height

#1,369,152

Difficulty

10.825564

Transactions

2

Size

935 B

Version

2

Bits

0ad3582b

Nonce

122,476,711

Timestamp

12/14/2015, 3:08:34 PM

Confirmations

5,457,564

Merkle Root

d2bf4fdae96f547e2b189c07ee755a311215a5be38cb5df155df5f12d7239d6c
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.

8.993 × 10⁹⁶(97-digit number)
89933401433497461848…86633106813663825919
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
8.993 × 10⁹⁶(97-digit number)
89933401433497461848…86633106813663825919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.798 × 10⁹⁷(98-digit number)
17986680286699492369…73266213627327651839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.597 × 10⁹⁷(98-digit number)
35973360573398984739…46532427254655303679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.194 × 10⁹⁷(98-digit number)
71946721146797969478…93064854509310607359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.438 × 10⁹⁸(99-digit number)
14389344229359593895…86129709018621214719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.877 × 10⁹⁸(99-digit number)
28778688458719187791…72259418037242429439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.755 × 10⁹⁸(99-digit number)
57557376917438375582…44518836074484858879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.151 × 10⁹⁹(100-digit number)
11511475383487675116…89037672148969717759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.302 × 10⁹⁹(100-digit number)
23022950766975350233…78075344297939435519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.604 × 10⁹⁹(100-digit number)
46045901533950700466…56150688595878871039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
9.209 × 10⁹⁹(100-digit number)
92091803067901400932…12301377191757742079
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:57,857,881 XPM·at block #6,826,715 · updates every 60s
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