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Block #2,461,900

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/7/2018, 2:17:58 PM Β· Difficulty 10.9562 Β· 4,383,491 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b7f357ae384ac1db58421d253ce23dfffc25cc7a7bc020d7a0e89b22182d7904
View on Chainz β†—

Height

#2,461,900

Difficulty

10.956216

Transactions

2

Size

392 B

Version

2

Bits

0af4ca93

Nonce

77,025,057

Timestamp

1/7/2018, 2:17:58 PM

Confirmations

4,383,491

Mined by

⛏️ P2SHAeCqimvwuWQzH2f1Uj3FFsEgusz17RDNFf

Merkle Root

0ad1fed2d134222baf5be6776768be97322a4b569d8fd631bdbce1a1b79efd03
Transactions (2)
Coinbase847cfb41952099…93aa85db8abfdb
1 in β†’ 1 out8.3300 XPM110 B
AeCqimvw…z17RDNFf
4e5a9f3b9e7cb7…1fa583f0c93999
1 in β†’ 1 out9.9900 XPM192 B
AYPS7P6G…PhQnkGZB
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.

1.255 Γ— 10⁹⁴(95-digit number)
12559062859537636858…93551186144796311039
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
1.255 Γ— 10⁹⁴(95-digit number)
12559062859537636858…93551186144796311039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.511 Γ— 10⁹⁴(95-digit number)
25118125719075273717…87102372289592622079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.023 Γ— 10⁹⁴(95-digit number)
50236251438150547434…74204744579185244159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁡(96-digit number)
10047250287630109486…48409489158370488319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.009 Γ— 10⁹⁡(96-digit number)
20094500575260218973…96818978316740976639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.018 Γ— 10⁹⁡(96-digit number)
40189001150520437947…93637956633481953279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.037 Γ— 10⁹⁡(96-digit number)
80378002301040875895…87275913266963906559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.607 Γ— 10⁹⁢(97-digit number)
16075600460208175179…74551826533927813119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.215 Γ— 10⁹⁢(97-digit number)
32151200920416350358…49103653067855626239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.430 Γ— 10⁹⁢(97-digit number)
64302401840832700716…98207306135711252479
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:58,007,574 XPMΒ·at block #6,845,390 Β· updates every 60s
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