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Block #2,276,533

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2017, 4:41:23 PM Β· Difficulty 10.9551 Β· 4,554,203 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
692daec61df5f594e7ae7471bec2e38bbd094a36836d03cc26e7b74c80e2562f
View on Chainz β†—

Height

#2,276,533

Difficulty

10.955133

Transactions

2

Size

426 B

Version

2

Bits

0af48399

Nonce

953,921,481

Timestamp

8/31/2017, 4:41:23 PM

Confirmations

4,554,203

Mined by

⛏️ P2SHAKuxcM9n7HaYMBzetyy6SR24T6EqFBUN4z

Merkle Root

723562b7bfcb6ba8f82c6b7bc8e6f0ba50f052d024f16c58e24c831a76a49244
Transactions (2)
Coinbase6c2f1eca0cf899…6d6d66e57a9a67
1 in β†’ 1 out8.3300 XPM109 B
AKuxcM9n…EqFBUN4z
31f230cb5dd8f5…0be4cb8b03f440
1 in β†’ 2 out794.6831 XPM227 B
AS8Swa5k…emSJQqiEANqH4nYX…8uvjFiGq
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.

1.053 Γ— 10⁹⁴(95-digit number)
10532516487446166152…00290388677212025961
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
1.053 Γ— 10⁹⁴(95-digit number)
10532516487446166152…00290388677212025961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.106 Γ— 10⁹⁴(95-digit number)
21065032974892332305…00580777354424051921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.213 Γ— 10⁹⁴(95-digit number)
42130065949784664610…01161554708848103841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.426 Γ— 10⁹⁴(95-digit number)
84260131899569329220…02323109417696207681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.685 Γ— 10⁹⁡(96-digit number)
16852026379913865844…04646218835392415361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.370 Γ— 10⁹⁡(96-digit number)
33704052759827731688…09292437670784830721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.740 Γ— 10⁹⁡(96-digit number)
67408105519655463376…18584875341569661441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.348 Γ— 10⁹⁢(97-digit number)
13481621103931092675…37169750683139322881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.696 Γ— 10⁹⁢(97-digit number)
26963242207862185350…74339501366278645761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.392 Γ— 10⁹⁢(97-digit number)
53926484415724370701…48679002732557291521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.078 Γ— 10⁹⁷(98-digit number)
10785296883144874140…97358005465114583041
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:57,890,025 XPMΒ·at block #6,830,735 Β· updates every 60s
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