Block #2,860,201

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/29/2018, 7:25:16 PM · Difficulty 11.6758 · 3,983,619 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6c61d0bfd601144811dab398f38a9cf53e749ed11a0ec5f187215bc56251914

Height

#2,860,201

Difficulty

11.675785

Transactions

2

Size

392 B

Version

2

Bits

0bad0038

Nonce

2,145,217,105

Timestamp

9/29/2018, 7:25:16 PM

Confirmations

3,983,619

Merkle Root

de7d9a602b9af67113315df3727e744d0b202b5bfd5e4497bb04c098e1b3a8eb
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.

1.602 × 10⁹⁵(96-digit number)
16023378860231224507…67036266725905985919
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
1.602 × 10⁹⁵(96-digit number)
16023378860231224507…67036266725905985919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.204 × 10⁹⁵(96-digit number)
32046757720462449014…34072533451811971839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.409 × 10⁹⁵(96-digit number)
64093515440924898029…68145066903623943679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.281 × 10⁹⁶(97-digit number)
12818703088184979605…36290133807247887359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.563 × 10⁹⁶(97-digit number)
25637406176369959211…72580267614495774719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.127 × 10⁹⁶(97-digit number)
51274812352739918423…45160535228991549439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.025 × 10⁹⁷(98-digit number)
10254962470547983684…90321070457983098879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.050 × 10⁹⁷(98-digit number)
20509924941095967369…80642140915966197759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.101 × 10⁹⁷(98-digit number)
41019849882191934738…61284281831932395519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
8.203 × 10⁹⁷(98-digit number)
82039699764383869477…22568563663864791039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.640 × 10⁹⁸(99-digit number)
16407939952876773895…45137127327729582079
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:57,994,937 XPM·at block #6,843,819 · updates every 60s
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