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Block #2,836,143

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 9/12/2018, 3:11:49 PM Β· Difficulty 11.7157 Β· 4,001,958 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2e6a1ffa0c34f604ce5405502e78bfdfd19eed9f4da9ba87d08d1698aad2e55
View on Chainz β†—

Height

#2,836,143

Difficulty

11.715679

Transactions

2

Size

722 B

Version

2

Bits

0bb736bf

Nonce

2,144,967,123

Timestamp

9/12/2018, 3:11:49 PM

Confirmations

4,001,958

Mined by

⛏️ P2SHAUhVx47gCXicPYzJu7iiXUiaGZgwkzMDGQ

Merkle Root

038c614f031a9c1d439e1e99494720d62e727bc823e41614eed573acf667f587
Transactions (2)
Coinbasea96bd65b906c38…a9e745b21e54fe
1 in β†’ 1 out7.2900 XPM110 B
AUhVx47g…gwkzMDGQ
d61cc4c3689f43…14655772ecb524
3 in β†’ 2 out188.8500 XPM523 B
APhbzzB3…3CPKstDTAJJJor7c…63AxCo4K
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.

2.318 Γ— 10⁹³(94-digit number)
23183867397027161800…29527723176874801921
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.318 Γ— 10⁹³(94-digit number)
23183867397027161800…29527723176874801921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.636 Γ— 10⁹³(94-digit number)
46367734794054323600…59055446353749603841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.273 Γ— 10⁹³(94-digit number)
92735469588108647201…18110892707499207681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.854 Γ— 10⁹⁴(95-digit number)
18547093917621729440…36221785414998415361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.709 Γ— 10⁹⁴(95-digit number)
37094187835243458880…72443570829996830721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.418 Γ— 10⁹⁴(95-digit number)
74188375670486917761…44887141659993661441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.483 Γ— 10⁹⁡(96-digit number)
14837675134097383552…89774283319987322881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.967 Γ— 10⁹⁡(96-digit number)
29675350268194767104…79548566639974645761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.935 Γ— 10⁹⁡(96-digit number)
59350700536389534208…59097133279949291521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.187 Γ— 10⁹⁢(97-digit number)
11870140107277906841…18194266559898583041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.374 Γ— 10⁹⁢(97-digit number)
23740280214555813683…36388533119797166081
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,949,161 XPMΒ·at block #6,838,100 Β· updates every 60s
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