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Block #2,854,621

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/25/2018, 1:39:59 PM Β· Difficulty 11.7078 Β· 3,983,401 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6174516dd841bfb45c0d2916200f161f384c79660b2ff1e5ac7d6da351400fc
View on Chainz β†—

Height

#2,854,621

Difficulty

11.707767

Transactions

2

Size

867 B

Version

2

Bits

0bb5303f

Nonce

977,618,127

Timestamp

9/25/2018, 1:39:59 PM

Confirmations

3,983,401

Mined by

⛏️ P2SHAH65pf7RQ9RGt5vbE87BMmZVZeDhtRnAhd

Merkle Root

6fc830a11702a73ba138346013c0b145f16ca057e57dd72d9cf9991e5b227fe2
Transactions (2)
Coinbase378a65ab790d48…3a6c92c43d88d4
1 in β†’ 1 out7.2900 XPM110 B
AH65pf7R…DhtRnAhd
e679a5b692394e…6708c1de9c9fa9
4 in β†’ 2 out51.1119 XPM668 B
AVx1qdeC…sU5DkantAHbTu9H8…PWUPVvNS
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.

1.438 Γ— 10⁹³(94-digit number)
14389349877982539735…07483216772088597759
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
1.438 Γ— 10⁹³(94-digit number)
14389349877982539735…07483216772088597759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.877 Γ— 10⁹³(94-digit number)
28778699755965079471…14966433544177195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.755 Γ— 10⁹³(94-digit number)
57557399511930158942…29932867088354391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁴(95-digit number)
11511479902386031788…59865734176708782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.302 Γ— 10⁹⁴(95-digit number)
23022959804772063577…19731468353417564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.604 Γ— 10⁹⁴(95-digit number)
46045919609544127154…39462936706835128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.209 Γ— 10⁹⁴(95-digit number)
92091839219088254308…78925873413670256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁡(96-digit number)
18418367843817650861…57851746827340513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.683 Γ— 10⁹⁡(96-digit number)
36836735687635301723…15703493654681026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.367 Γ— 10⁹⁡(96-digit number)
73673471375270603446…31406987309362053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.473 Γ— 10⁹⁢(97-digit number)
14734694275054120689…62813974618724106239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,948,531 XPMΒ·at block #6,838,021 Β· updates every 60s
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