Block #1,416,951

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/17/2016, 10:08:49 AM · Difficulty 10.7946 · 5,423,315 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
437601c961447fddb95334e8a9978ba82e484aeaa8742e90127a23c3331c2655

Height

#1,416,951

Difficulty

10.794627

Transactions

3

Size

958 B

Version

2

Bits

0acb6ca8

Nonce

377,393,357

Timestamp

1/17/2016, 10:08:49 AM

Confirmations

5,423,315

Merkle Root

1b4f7f6a4cdd2183b1cae9226a730bbc02b8dcf77eb4934debae77dca096c025
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.

5.952 × 10⁹⁵(96-digit number)
59528727497995674566…18160517654538066241
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
5.952 × 10⁹⁵(96-digit number)
59528727497995674566…18160517654538066241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.190 × 10⁹⁶(97-digit number)
11905745499599134913…36321035309076132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.381 × 10⁹⁶(97-digit number)
23811490999198269826…72642070618152264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.762 × 10⁹⁶(97-digit number)
47622981998396539653…45284141236304529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.524 × 10⁹⁶(97-digit number)
95245963996793079306…90568282472609059841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.904 × 10⁹⁷(98-digit number)
19049192799358615861…81136564945218119681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.809 × 10⁹⁷(98-digit number)
38098385598717231722…62273129890436239361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.619 × 10⁹⁷(98-digit number)
76196771197434463444…24546259780872478721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.523 × 10⁹⁸(99-digit number)
15239354239486892688…49092519561744957441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.047 × 10⁹⁸(99-digit number)
30478708478973785377…98185039123489914881
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:57,966,442 XPM·at block #6,840,265 · updates every 60s
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