Block #2,925,454

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/16/2018, 1:18:55 PM · Difficulty 11.3544 · 3,915,008 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4d72ea41e37a74f200fd67d737f6d0b8d9b6df7de33901fdef0461b50d05e4ab

Height

#2,925,454

Difficulty

11.354439

Transactions

11

Size

72.89 KB

Version

2

Bits

0b5abc8a

Nonce

1,163,602,984

Timestamp

11/16/2018, 1:18:55 PM

Confirmations

3,915,008

Merkle Root

b09cea66dc370705786794fbd6f57cff454a8fea5eea5b75e27c3f25676c272b
Transactions (11)
1 in → 1 out8.5400 XPM109 B
50 in → 1 out231.0294 XPM7.27 KB
50 in → 1 out221.1887 XPM7.27 KB
50 in → 1 out214.7878 XPM7.27 KB
50 in → 1 out220.1175 XPM7.27 KB
50 in → 1 out244.6723 XPM7.26 KB
50 in → 1 out220.3370 XPM7.27 KB
50 in → 1 out222.9830 XPM7.27 KB
50 in → 1 out206.3979 XPM7.27 KB
50 in → 1 out203.0017 XPM7.27 KB
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.

5.835 × 10⁹⁶(97-digit number)
58359960581270168129…82066449467453644799
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
5.835 × 10⁹⁶(97-digit number)
58359960581270168129…82066449467453644799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.167 × 10⁹⁷(98-digit number)
11671992116254033625…64132898934907289599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.334 × 10⁹⁷(98-digit number)
23343984232508067251…28265797869814579199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.668 × 10⁹⁷(98-digit number)
46687968465016134503…56531595739629158399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.337 × 10⁹⁷(98-digit number)
93375936930032269007…13063191479258316799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.867 × 10⁹⁸(99-digit number)
18675187386006453801…26126382958516633599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.735 × 10⁹⁸(99-digit number)
37350374772012907603…52252765917033267199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.470 × 10⁹⁸(99-digit number)
74700749544025815206…04505531834066534399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.494 × 10⁹⁹(100-digit number)
14940149908805163041…09011063668133068799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.988 × 10⁹⁹(100-digit number)
29880299817610326082…18022127336266137599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.976 × 10⁹⁹(100-digit number)
59760599635220652165…36044254672532275199
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:57,968,024 XPM·at block #6,840,461 · updates every 60s
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