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Block #2,658,126

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/12/2018, 2:31:22 PM Β· Difficulty 11.6567 Β· 4,172,397 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5bf717b2175027d6e6cf4437e7b9c1863458717d481128577f298ad46a3201f8
View on Chainz β†—

Height

#2,658,126

Difficulty

11.656653

Transactions

2

Size

2.29 KB

Version

2

Bits

0ba81a6f

Nonce

712,877,133

Timestamp

5/12/2018, 2:31:22 PM

Confirmations

4,172,397

Mined by

⛏️ P2SHAdbLMxd4dSNi5oyy7D6WnGsPTBqBYJ9QkJ

Merkle Root

0f6fa6767ecb40f420e7f879fa4e87a2fc26d6bcb4a06297586469444463f2c1
Transactions (2)
Coinbasead24bf50248aa3…54bcabf8794673
1 in β†’ 1 out7.3800 XPM109 B
AdbLMxd4…qBYJ9QkJ
9005914e279374…9369d4e928ddca
14 in β†’ 2 out81.0853 XPM2.10 KB
AKwzttu4…6QdD8QUVANrcyBdq…fxFf32RZ
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.

5.236 Γ— 10⁹¹(92-digit number)
52366040240098960403…35584531339074509391
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
5.236 Γ— 10⁹¹(92-digit number)
52366040240098960403…35584531339074509391
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.047 Γ— 10⁹²(93-digit number)
10473208048019792080…71169062678149018781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.094 Γ— 10⁹²(93-digit number)
20946416096039584161…42338125356298037561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.189 Γ— 10⁹²(93-digit number)
41892832192079168322…84676250712596075121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.378 Γ— 10⁹²(93-digit number)
83785664384158336645…69352501425192150241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.675 Γ— 10⁹³(94-digit number)
16757132876831667329…38705002850384300481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.351 Γ— 10⁹³(94-digit number)
33514265753663334658…77410005700768600961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.702 Γ— 10⁹³(94-digit number)
67028531507326669316…54820011401537201921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.340 Γ— 10⁹⁴(95-digit number)
13405706301465333863…09640022803074403841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.681 Γ— 10⁹⁴(95-digit number)
26811412602930667726…19280045606148807681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
5.362 Γ— 10⁹⁴(95-digit number)
53622825205861335453…38560091212297615361
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:57,888,436 XPMΒ·at block #6,830,522 Β· updates every 60s
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