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Block #1,109,875

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 6/16/2015, 11:07:37 AM Β· Difficulty 10.8636 Β· 5,703,984 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a105d49595e052411c5e4df1b8bc85b4457fb7b06e29bdecf29a5e4814616aa
View on Chainz β†—

Height

#1,109,875

Difficulty

10.863615

Transactions

2

Size

836 B

Version

2

Bits

0add15e0

Nonce

136,500,192

Timestamp

6/16/2015, 11:07:37 AM

Confirmations

5,703,984

Mined by

⛏️ P2SHAM971N7VTy7FPmJ2KTaiYazpK5VuBMD6mR

Merkle Root

052dd70d0e96fdcd5c4b959676b93e609b08aea15f8d222f26d562ec50f467e6
Transactions (2)
Coinbasecbe78967e05380…00a5dc031a05b1
1 in β†’ 1 out8.4700 XPM110 B
AM971N7V…VuBMD6mR
d5a0167abe191d…b52a3e60ebecc4
4 in β†’ 1 out1.8478 XPM636 B
Acb1xA8z…9ActivN8
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.

1.210 Γ— 10⁹⁴(95-digit number)
12100095582681342748…48363826127270166331
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
1.210 Γ— 10⁹⁴(95-digit number)
12100095582681342748…48363826127270166331
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.420 Γ— 10⁹⁴(95-digit number)
24200191165362685496…96727652254540332661
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.840 Γ— 10⁹⁴(95-digit number)
48400382330725370993…93455304509080665321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.680 Γ— 10⁹⁴(95-digit number)
96800764661450741986…86910609018161330641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.936 Γ— 10⁹⁡(96-digit number)
19360152932290148397…73821218036322661281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.872 Γ— 10⁹⁡(96-digit number)
38720305864580296794…47642436072645322561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.744 Γ— 10⁹⁡(96-digit number)
77440611729160593589…95284872145290645121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.548 Γ— 10⁹⁢(97-digit number)
15488122345832118717…90569744290581290241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.097 Γ— 10⁹⁢(97-digit number)
30976244691664237435…81139488581162580481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.195 Γ— 10⁹⁢(97-digit number)
61952489383328474871…62278977162325160961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.239 Γ— 10⁹⁷(98-digit number)
12390497876665694974…24557954324650321921
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:57,754,944 XPMΒ·at block #6,813,858 Β· updates every 60s
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