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Block #2,655,112

2CCLength 12β˜…β˜…β˜…β˜…β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/9/2018, 9:56:11 PM Β· Difficulty 11.7104 Β· 4,177,594 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ecb16e4b21cb187ce9a7c60a63f2bcd77ff600087d545dbb7c5cd30bb764b3ee
View on Chainz β†—

Height

#2,655,112

Difficulty

11.710411

Transactions

2

Size

1.00 KB

Version

2

Bits

0bb5dd79

Nonce

486,063,863

Timestamp

5/9/2018, 9:56:11 PM

Confirmations

4,177,594

Mined by

⛏️ P2SHAKgc6DLVBsnGGt517ZhPCsQas1i1DMVwgo

Merkle Root

2a065f790884926ed31fb5e670c72e20b97da7dd3d1ae06f8ed1c667b3ebb533
Transactions (2)
Coinbase41295ac4d6f19c…94d5eb7aca9348
1 in β†’ 1 out7.2900 XPM110 B
AKgc6DLV…i1DMVwgo
b32afaa4c475ac…7154616e19d555
6 in β†’ 2 out34.9471 XPM829 B
AWp4iAg7…FUBLEm8xAGvsi9Qw…jWaVCFXV
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.

5.761 Γ— 10⁹⁡(96-digit number)
57615501237056655754…02452935205194853761
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
5.761 Γ— 10⁹⁡(96-digit number)
57615501237056655754…02452935205194853761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.152 Γ— 10⁹⁢(97-digit number)
11523100247411331150…04905870410389707521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.304 Γ— 10⁹⁢(97-digit number)
23046200494822662301…09811740820779415041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.609 Γ— 10⁹⁢(97-digit number)
46092400989645324603…19623481641558830081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
9.218 Γ— 10⁹⁢(97-digit number)
92184801979290649207…39246963283117660161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.843 Γ— 10⁹⁷(98-digit number)
18436960395858129841…78493926566235320321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.687 Γ— 10⁹⁷(98-digit number)
36873920791716259682…56987853132470640641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
7.374 Γ— 10⁹⁷(98-digit number)
73747841583432519365…13975706264941281281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.474 Γ— 10⁹⁸(99-digit number)
14749568316686503873…27951412529882562561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.949 Γ— 10⁹⁸(99-digit number)
29499136633373007746…55902825059765125121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.899 Γ— 10⁹⁸(99-digit number)
58998273266746015492…11805650119530250241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
12
2^11 Γ— origin + 1
1.179 Γ— 10⁹⁹(100-digit number)
11799654653349203098…23611300239060500481
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,905,806 XPMΒ·at block #6,832,705 Β· updates every 60s
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