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Block #258,071

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/12/2013, 8:13:37 PM Β· Difficulty 9.9762 Β· 6,545,249 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
65d214477891cce684dda7d222e6f426f21269a0b2e602dac999e743c417753f
View on Chainz β†—

Height

#258,071

Difficulty

9.976204

Transactions

1

Size

2.14 KB

Version

2

Bits

09f9e888

Nonce

48,373

Timestamp

11/12/2013, 8:13:37 PM

Confirmations

6,545,249

Mined by

⛏️ aRANuKx9Kemb4q2j6b7vjmfuKrAuwm7nrBRq

Merkle Root

ad622f07f7acd999fa0053d2e739e2aff4853f1603d09a6cea5b080150fb61f5
Transactions (1)
Coinbasead622f07f7acd9…5b080150fb61f5
1 in β†’ 60 out10.0000 XPM2.05 KB
ANuKx9Ke…wm7nrBRqAQtzUSwq…htAuF3yCARR7aRH6…ne3DXGXZAeNjg8HA…9AkdpcSCAU9KdB9r…o5XC6WMy
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.458 Γ— 10⁹³(94-digit number)
14581912846947019911…53394339778106256319
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.458 Γ— 10⁹³(94-digit number)
14581912846947019911…53394339778106256319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.916 Γ— 10⁹³(94-digit number)
29163825693894039822…06788679556212512639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.832 Γ— 10⁹³(94-digit number)
58327651387788079644…13577359112425025279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.166 Γ— 10⁹⁴(95-digit number)
11665530277557615928…27154718224850050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.333 Γ— 10⁹⁴(95-digit number)
23331060555115231857…54309436449700101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.666 Γ— 10⁹⁴(95-digit number)
46662121110230463715…08618872899400202239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.332 Γ— 10⁹⁴(95-digit number)
93324242220460927431…17237745798800404479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.866 Γ— 10⁹⁡(96-digit number)
18664848444092185486…34475491597600808959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.732 Γ— 10⁹⁡(96-digit number)
37329696888184370972…68950983195201617919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.465 Γ— 10⁹⁡(96-digit number)
74659393776368741945…37901966390403235839
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,670,589 XPMΒ·at block #6,803,319 Β· updates every 60s
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