Block #1,965,426

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 2/2/2017, 6:24:52 AM · Difficulty 10.7498 · 4,861,710 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5a6f06d2778ca49b14a8e5fb4a30b02cacdc6f5b9dc264448db13d8b947c1281

Height

#1,965,426

Difficulty

10.749796

Transactions

2

Size

1022 B

Version

2

Bits

0abff29b

Nonce

2,013,655,494

Timestamp

2/2/2017, 6:24:52 AM

Confirmations

4,861,710

Merkle Root

0d9bf3ff70d5a4e6b44bda130b134279b38a2bfe6c7084a1707f10e3e1dca52c
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.

2.179 × 10⁹⁶(97-digit number)
21799832160696800420…71083378890441615359
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
2.179 × 10⁹⁶(97-digit number)
21799832160696800420…71083378890441615359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.359 × 10⁹⁶(97-digit number)
43599664321393600841…42166757780883230719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.719 × 10⁹⁶(97-digit number)
87199328642787201683…84333515561766461439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.743 × 10⁹⁷(98-digit number)
17439865728557440336…68667031123532922879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.487 × 10⁹⁷(98-digit number)
34879731457114880673…37334062247065845759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.975 × 10⁹⁷(98-digit number)
69759462914229761346…74668124494131691519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.395 × 10⁹⁸(99-digit number)
13951892582845952269…49336248988263383039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.790 × 10⁹⁸(99-digit number)
27903785165691904538…98672497976526766079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.580 × 10⁹⁸(99-digit number)
55807570331383809077…97344995953053532159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.116 × 10⁹⁹(100-digit number)
11161514066276761815…94689991906107064319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.232 × 10⁹⁹(100-digit number)
22323028132553523630…89379983812214128639
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:57,861,269 XPM·at block #6,827,135 · updates every 60s
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