Block #1,983,754

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/15/2017, 12:38:14 AM · Difficulty 10.7481 · 4,861,087 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
636a5815a704279480df402c9d69781fd5c7f3e4a1ce7f5cc93cee945041b9d4

Height

#1,983,754

Difficulty

10.748138

Transactions

2

Size

698 B

Version

2

Bits

0abf85f7

Nonce

1,157,445,624

Timestamp

2/15/2017, 12:38:14 AM

Confirmations

4,861,087

Merkle Root

c09c4e9c4b57b2488ef1b50a0877a183fe16e4718757778b624173d2a6b35902
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.

2.499 × 10⁹⁶(97-digit number)
24992146243345742867…71002757703381713921
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
2.499 × 10⁹⁶(97-digit number)
24992146243345742867…71002757703381713921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.998 × 10⁹⁶(97-digit number)
49984292486691485734…42005515406763427841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.996 × 10⁹⁶(97-digit number)
99968584973382971468…84011030813526855681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.999 × 10⁹⁷(98-digit number)
19993716994676594293…68022061627053711361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.998 × 10⁹⁷(98-digit number)
39987433989353188587…36044123254107422721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.997 × 10⁹⁷(98-digit number)
79974867978706377175…72088246508214845441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.599 × 10⁹⁸(99-digit number)
15994973595741275435…44176493016429690881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.198 × 10⁹⁸(99-digit number)
31989947191482550870…88352986032859381761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.397 × 10⁹⁸(99-digit number)
63979894382965101740…76705972065718763521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.279 × 10⁹⁹(100-digit number)
12795978876593020348…53411944131437527041
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:58,003,137 XPM·at block #6,844,840 · updates every 60s
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