Block #375,337

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/25/2014, 3:47:14 PM · Difficulty 10.4232 · 6,421,476 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aec4ca9f6d3b5ecdd1ce5964b1bc6d9052fecd90729195c0e577980d79dbf26f

Height

#375,337

Difficulty

10.423170

Transactions

2

Size

434 B

Version

2

Bits

0a6c54e0

Nonce

1,949

Timestamp

1/25/2014, 3:47:14 PM

Confirmations

6,421,476

Merkle Root

b74b62953442d6ee9684ce3c9e6445fbf39351f2914424358d6483ca49d4a6be
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.

3.725 × 10⁹⁹(100-digit number)
37253066925390219394…64845094891973918719
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
3.725 × 10⁹⁹(100-digit number)
37253066925390219394…64845094891973918719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.450 × 10⁹⁹(100-digit number)
74506133850780438789…29690189783947837439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.490 × 10¹⁰⁰(101-digit number)
14901226770156087757…59380379567895674879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.980 × 10¹⁰⁰(101-digit number)
29802453540312175515…18760759135791349759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.960 × 10¹⁰⁰(101-digit number)
59604907080624351031…37521518271582699519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.192 × 10¹⁰¹(102-digit number)
11920981416124870206…75043036543165399039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.384 × 10¹⁰¹(102-digit number)
23841962832249740412…50086073086330798079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.768 × 10¹⁰¹(102-digit number)
47683925664499480825…00172146172661596159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.536 × 10¹⁰¹(102-digit number)
95367851328998961650…00344292345323192319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.907 × 10¹⁰²(103-digit number)
19073570265799792330…00688584690646384639
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 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
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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,618,512 XPM·at block #6,796,812 · updates every 60s
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