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Block #2,833,216

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 2:30:43 PM Β· Difficulty 11.7151 Β· 4,008,153 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
73036423cb87a7519e2a728a8763a1fc105d8c8b527fd83d25cd62670a72941a
View on Chainz β†—

Height

#2,833,216

Difficulty

11.715109

Transactions

1

Size

200 B

Version

2

Bits

0bb7115c

Nonce

894,635,211

Timestamp

9/10/2018, 2:30:43 PM

Confirmations

4,008,153

Mined by

⛏️ P2SHAL7mkPg8FVrmRLno6HGWauAr1rvA3Xof4N

Merkle Root

3d0d6ba16f6301d9ddeb1d65fb4074fcab99e2be5183a130ba11577fe1e1e2a8
Transactions (1)
Coinbase3d0d6ba16f6301…11577fe1e1e2a8
1 in β†’ 1 out7.2700 XPM109 B
AL7mkPg8…vA3Xof4N
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.

7.964 Γ— 10⁹⁢(97-digit number)
79642287379268757573…60187329826711551999
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
7.964 Γ— 10⁹⁢(97-digit number)
79642287379268757573…60187329826711551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.592 Γ— 10⁹⁷(98-digit number)
15928457475853751514…20374659653423103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.185 Γ— 10⁹⁷(98-digit number)
31856914951707503029…40749319306846207999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.371 Γ— 10⁹⁷(98-digit number)
63713829903415006058…81498638613692415999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.274 Γ— 10⁹⁸(99-digit number)
12742765980683001211…62997277227384831999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.548 Γ— 10⁹⁸(99-digit number)
25485531961366002423…25994554454769663999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.097 Γ— 10⁹⁸(99-digit number)
50971063922732004847…51989108909539327999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.019 Γ— 10⁹⁹(100-digit number)
10194212784546400969…03978217819078655999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.038 Γ— 10⁹⁹(100-digit number)
20388425569092801938…07956435638157311999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.077 Γ— 10⁹⁹(100-digit number)
40776851138185603877…15912871276314623999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.155 Γ— 10⁹⁹(100-digit number)
81553702276371207755…31825742552629247999
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:57,975,322 XPMΒ·at block #6,841,368 Β· updates every 60s
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