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Block #115,994

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/14/2013, 3:37:20 AM Β· Difficulty 9.7457 Β· 6,680,403 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4e0d4e9c4848356ca80bea299512c0ab8fd5f247307cb94e499f4b9a22bca404
View on Chainz β†—

Height

#115,994

Difficulty

9.745715

Transactions

1

Size

202 B

Version

2

Bits

09bee727

Nonce

1,408,371

Timestamp

8/14/2013, 3:37:20 AM

Confirmations

6,680,403

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

b54f8ca84672625c812fc4f56a443b9250276228ef2ad86d441771e4028ea4d0
Transactions (1)
Coinbaseb54f8ca8467262…1771e4028ea4d0
1 in β†’ 1 out10.5100 XPM112 B
AT5A2KL6…CT16n6i2
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.

2.729 Γ— 10⁹⁴(95-digit number)
27296264556532965192…18170271166564518241
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
2.729 Γ— 10⁹⁴(95-digit number)
27296264556532965192…18170271166564518241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.459 Γ— 10⁹⁴(95-digit number)
54592529113065930385…36340542333129036481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.091 Γ— 10⁹⁡(96-digit number)
10918505822613186077…72681084666258072961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.183 Γ— 10⁹⁡(96-digit number)
21837011645226372154…45362169332516145921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.367 Γ— 10⁹⁡(96-digit number)
43674023290452744308…90724338665032291841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.734 Γ— 10⁹⁡(96-digit number)
87348046580905488617…81448677330064583681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.746 Γ— 10⁹⁢(97-digit number)
17469609316181097723…62897354660129167361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.493 Γ— 10⁹⁢(97-digit number)
34939218632362195447…25794709320258334721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.987 Γ— 10⁹⁢(97-digit number)
69878437264724390894…51589418640516669441
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,615,173 XPMΒ·at block #6,796,396 Β· updates every 60s
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