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Block #2,294,102

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2017, 2:00:49 AM Β· Difficulty 10.9532 Β· 4,549,782 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
af775b0ba2625291e979c23f86f0e75a28e80c5457123b03c0cc9ac5d3315c1c
View on Chainz β†—

Height

#2,294,102

Difficulty

10.953208

Transactions

2

Size

392 B

Version

2

Bits

0af40570

Nonce

374,073,710

Timestamp

9/13/2017, 2:00:49 AM

Confirmations

4,549,782

Mined by

⛏️ P2SHAHEnfNRiYJJURKTayTQzAf9Hofnfhv8pLs

Merkle Root

a1bf6e3419bd06c1ca2a26e0f0cf5cf8ced8cd569c2cdbad3dbb856e2ef0624f
Transactions (2)
Coinbasef4132cdefff153…240577411f37ae
1 in β†’ 1 out8.3300 XPM110 B
AHEnfNRi…nfhv8pLs
fbc2cd3513c25e…4e1c2c2d6e352a
1 in β†’ 1 out99.9900 XPM192 B
ARsuhVkc…w3M6D8DV
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.

5.272 Γ— 10⁹⁴(95-digit number)
52720598915412898563…89571476791350975999
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
5.272 Γ— 10⁹⁴(95-digit number)
52720598915412898563…89571476791350975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.054 Γ— 10⁹⁡(96-digit number)
10544119783082579712…79142953582701951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.108 Γ— 10⁹⁡(96-digit number)
21088239566165159425…58285907165403903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.217 Γ— 10⁹⁡(96-digit number)
42176479132330318850…16571814330807807999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.435 Γ— 10⁹⁡(96-digit number)
84352958264660637701…33143628661615615999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.687 Γ— 10⁹⁢(97-digit number)
16870591652932127540…66287257323231231999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.374 Γ— 10⁹⁢(97-digit number)
33741183305864255080…32574514646462463999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.748 Γ— 10⁹⁢(97-digit number)
67482366611728510161…65149029292924927999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.349 Γ— 10⁹⁷(98-digit number)
13496473322345702032…30298058585849855999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.699 Γ— 10⁹⁷(98-digit number)
26992946644691404064…60596117171699711999
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:57,995,440 XPMΒ·at block #6,843,883 Β· updates every 60s
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