Block #1,937,050

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/13/2017, 6:34:57 AM · Difficulty 10.7685 · 4,900,656 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ff77676ac35bc8cefc5e1745e1cfdc6f0868a4360f19768c4828e4b30c6fee15

Height

#1,937,050

Difficulty

10.768502

Transactions

4

Size

6.49 KB

Version

2

Bits

0ac4bc8c

Nonce

1,155,453,413

Timestamp

1/13/2017, 6:34:57 AM

Confirmations

4,900,656

Merkle Root

e2488062186a8d0fd087ca2e337ecfffee4d13df716f54447c61135ab5584f1c
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.

2.010 × 10⁹³(94-digit number)
20104654584031388257…70822765098902449221
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
2.010 × 10⁹³(94-digit number)
20104654584031388257…70822765098902449221
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.020 × 10⁹³(94-digit number)
40209309168062776515…41645530197804898441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.041 × 10⁹³(94-digit number)
80418618336125553031…83291060395609796881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.608 × 10⁹⁴(95-digit number)
16083723667225110606…66582120791219593761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.216 × 10⁹⁴(95-digit number)
32167447334450221212…33164241582439187521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.433 × 10⁹⁴(95-digit number)
64334894668900442425…66328483164878375041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.286 × 10⁹⁵(96-digit number)
12866978933780088485…32656966329756750081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.573 × 10⁹⁵(96-digit number)
25733957867560176970…65313932659513500161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.146 × 10⁹⁵(96-digit number)
51467915735120353940…30627865319027000321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.029 × 10⁹⁶(97-digit number)
10293583147024070788…61255730638054000641
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:57,945,974 XPM·at block #6,837,705 · updates every 60s
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