Block #2,016,919

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/10/2017, 12:26:40 PM · Difficulty 10.7146 · 4,794,156 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
70376ac1cbc07d4532bb8f52725f3d89760da0073ec88eb18498e40884f86817

Height

#2,016,919

Difficulty

10.714563

Transactions

4

Size

3.16 KB

Version

2

Bits

0ab6ed96

Nonce

723,904,939

Timestamp

3/10/2017, 12:26:40 PM

Confirmations

4,794,156

Merkle Root

a02dfb8fd3a4767bffaaeac9a7b9e839f63d1b556416c80f80a632d424f95296
Transactions (4)
1 in → 1 out8.7500 XPM109 B
8 in → 1 out52.0000 XPM1.03 KB
5 in → 1 out20.0000 XPM715 B
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.

8.632 × 10⁹⁶(97-digit number)
86322625883536314411…15555499938542233599
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
8.632 × 10⁹⁶(97-digit number)
86322625883536314411…15555499938542233599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.726 × 10⁹⁷(98-digit number)
17264525176707262882…31110999877084467199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.452 × 10⁹⁷(98-digit number)
34529050353414525764…62221999754168934399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.905 × 10⁹⁷(98-digit number)
69058100706829051528…24443999508337868799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.381 × 10⁹⁸(99-digit number)
13811620141365810305…48887999016675737599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.762 × 10⁹⁸(99-digit number)
27623240282731620611…97775998033351475199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.524 × 10⁹⁸(99-digit number)
55246480565463241223…95551996066702950399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.104 × 10⁹⁹(100-digit number)
11049296113092648244…91103992133405900799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.209 × 10⁹⁹(100-digit number)
22098592226185296489…82207984266811801599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.419 × 10⁹⁹(100-digit number)
44197184452370592978…64415968533623603199
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:57,732,705 XPM·at block #6,811,074 · updates every 60s
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