Block #377,060

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/26/2014, 8:12:26 PM · Difficulty 10.4255 · 6,428,140 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
def56f1904d33ac9a3e5e078f230857c24146bace5af6c2a84bfa12fe924b928

Height

#377,060

Difficulty

10.425542

Transactions

4

Size

1.44 KB

Version

2

Bits

0a6cf056

Nonce

26,084

Timestamp

1/26/2014, 8:12:26 PM

Confirmations

6,428,140

Merkle Root

32d4b2de5d1bd7d8fce3426ced6e642dcd8e513c00796c3af7e975a1cba5b2db
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.

5.768 × 10⁹⁹(100-digit number)
57685361956196698659…99210807334214072319
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
5.768 × 10⁹⁹(100-digit number)
57685361956196698659…99210807334214072319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.153 × 10¹⁰⁰(101-digit number)
11537072391239339731…98421614668428144639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.307 × 10¹⁰⁰(101-digit number)
23074144782478679463…96843229336856289279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.614 × 10¹⁰⁰(101-digit number)
46148289564957358927…93686458673712578559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
9.229 × 10¹⁰⁰(101-digit number)
92296579129914717855…87372917347425157119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.845 × 10¹⁰¹(102-digit number)
18459315825982943571…74745834694850314239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.691 × 10¹⁰¹(102-digit number)
36918631651965887142…49491669389700628479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
7.383 × 10¹⁰¹(102-digit number)
73837263303931774284…98983338779401256959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.476 × 10¹⁰²(103-digit number)
14767452660786354856…97966677558802513919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.953 × 10¹⁰²(103-digit number)
29534905321572709713…95933355117605027839
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:57,685,670 XPM·at block #6,805,199 · updates every 60s
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