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Block #911,102

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/26/2015, 8:10:10 PM Β· Difficulty 10.9318 Β· 5,888,246 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3290c973e95b0347e4cb281385a836a944d486e9c4be1af119c88e29c828660b
View on Chainz β†—

Height

#911,102

Difficulty

10.931837

Transactions

2

Size

3.86 KB

Version

2

Bits

0aee8cdf

Nonce

569,097,374

Timestamp

1/26/2015, 8:10:10 PM

Confirmations

5,888,246

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

43fcb899859ced347b3c06ee23ad1c075f8b0c86e0d195e27902a882eda69f45
Transactions (2)
Coinbaseb8aae011eaaa75…4225cfcf7e8c04
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
1d8b4a5091cb6b…8a2c3eee6564a4
25 in β†’ 1 out3484.9100 XPM3.65 KB
AGcN2N4H…7yjnwxnk
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.

3.602 Γ— 10⁹⁡(96-digit number)
36025923658790383385…57898896206999616601
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
3.602 Γ— 10⁹⁡(96-digit number)
36025923658790383385…57898896206999616601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.205 Γ— 10⁹⁡(96-digit number)
72051847317580766771…15797792413999233201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.441 Γ— 10⁹⁢(97-digit number)
14410369463516153354…31595584827998466401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.882 Γ— 10⁹⁢(97-digit number)
28820738927032306708…63191169655996932801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
5.764 Γ— 10⁹⁢(97-digit number)
57641477854064613417…26382339311993865601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.152 Γ— 10⁹⁷(98-digit number)
11528295570812922683…52764678623987731201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.305 Γ— 10⁹⁷(98-digit number)
23056591141625845367…05529357247975462401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.611 Γ— 10⁹⁷(98-digit number)
46113182283251690734…11058714495950924801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.222 Γ— 10⁹⁷(98-digit number)
92226364566503381468…22117428991901849601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.844 Γ— 10⁹⁸(99-digit number)
18445272913300676293…44234857983803699201
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,638,836 XPMΒ·at block #6,799,347 Β· updates every 60s
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