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Block #816,127

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/18/2014, 1:37:38 AM Β· Difficulty 10.9750 Β· 6,020,682 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d38102407e17495c25d13566f2a358753a21271b26e3ae00c3483d4b09266a08
View on Chainz β†—

Height

#816,127

Difficulty

10.974966

Transactions

2

Size

729 B

Version

2

Bits

0af99760

Nonce

211,307,685

Timestamp

11/18/2014, 1:37:38 AM

Confirmations

6,020,682

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fc66331620cce656da059f5452c6a8871d03a110bbf670b77ccbd607428cf230
Transactions (2)
Coinbasea89a974557f7b0…3d5378bbe7d773
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
7ec7abaabd1d80…16fa7b2dc8370a
3 in β†’ 2 out999.8721 XPM523 B
AUFqxfHA…RSjoNb6vATm87ZgM…TU4ZS5nf
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.

2.987 Γ— 10⁹⁡(96-digit number)
29872455296243732545…62103311842423283601
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
2.987 Γ— 10⁹⁡(96-digit number)
29872455296243732545…62103311842423283601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.974 Γ— 10⁹⁡(96-digit number)
59744910592487465091…24206623684846567201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.194 Γ— 10⁹⁢(97-digit number)
11948982118497493018…48413247369693134401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.389 Γ— 10⁹⁢(97-digit number)
23897964236994986036…96826494739386268801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.779 Γ— 10⁹⁢(97-digit number)
47795928473989972072…93652989478772537601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.559 Γ— 10⁹⁢(97-digit number)
95591856947979944145…87305978957545075201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.911 Γ— 10⁹⁷(98-digit number)
19118371389595988829…74611957915090150401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.823 Γ— 10⁹⁷(98-digit number)
38236742779191977658…49223915830180300801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.647 Γ— 10⁹⁷(98-digit number)
76473485558383955316…98447831660360601601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.529 Γ— 10⁹⁸(99-digit number)
15294697111676791063…96895663320721203201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
3.058 Γ— 10⁹⁸(99-digit number)
30589394223353582126…93791326641442406401
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:57,938,755 XPMΒ·at block #6,836,808 Β· updates every 60s
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