Block #2,455,616

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 1/3/2018, 11:14:04 AM · Difficulty 10.9530 · 4,389,764 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
204391cdc74f8d4021ccb362f94c8025253c86a14e21df4e12b9b0257852682d

Height

#2,455,616

Difficulty

10.952959

Transactions

2

Size

424 B

Version

2

Bits

0af3f521

Nonce

839,856,857

Timestamp

1/3/2018, 11:14:04 AM

Confirmations

4,389,764

Merkle Root

66bc343910d48c0295afdc70b944b4fd32ef2a2424d823f4493bd4b525489bc0
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.

5.274 × 10⁹⁴(95-digit number)
52745401343561045719…44555229613121686239
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
5.274 × 10⁹⁴(95-digit number)
52745401343561045719…44555229613121686239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.054 × 10⁹⁵(96-digit number)
10549080268712209143…89110459226243372479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.109 × 10⁹⁵(96-digit number)
21098160537424418287…78220918452486744959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.219 × 10⁹⁵(96-digit number)
42196321074848836575…56441836904973489919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.439 × 10⁹⁵(96-digit number)
84392642149697673150…12883673809946979839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.687 × 10⁹⁶(97-digit number)
16878528429939534630…25767347619893959679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.375 × 10⁹⁶(97-digit number)
33757056859879069260…51534695239787919359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.751 × 10⁹⁶(97-digit number)
67514113719758138520…03069390479575838719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.350 × 10⁹⁷(98-digit number)
13502822743951627704…06138780959151677439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.700 × 10⁹⁷(98-digit number)
27005645487903255408…12277561918303354879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.401 × 10⁹⁷(98-digit number)
54011290975806510816…24555123836606709759
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:58,007,485 XPM·at block #6,845,379 · updates every 60s
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