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Block #1,894,922

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/15/2016, 7:07:34 AM Β· Difficulty 10.7477 Β· 4,919,045 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
03a3af6ad2dcf861fcebf87a7ae0361520be242ee98bac47036828f27c5e3c4c
View on Chainz β†—

Height

#1,894,922

Difficulty

10.747719

Transactions

2

Size

1.14 KB

Version

2

Bits

0abf6a86

Nonce

665,733,885

Timestamp

12/15/2016, 7:07:34 AM

Confirmations

4,919,045

Mined by

⛏️ P2SHAR2sK6WrYeCfAnLFpuTKFMHB9CrXsT6oPB

Merkle Root

e6ce318e8ca887a74763609f76bc0080db0cc531c7733457338b4f7fff5fd8e7
Transactions (2)
Coinbaseea799d7feec375…0d5829fe2b472a
1 in β†’ 1 out8.6500 XPM109 B
AR2sK6Wr…rXsT6oPB
a67b936cb870e6…e7fb89b58c2298
6 in β†’ 2 out10.7820 XPM967 B
ASMMZz4E…7FeHYYcpAMWuVh9Y…KuZuEwkF
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.

1.117 Γ— 10⁹⁴(95-digit number)
11177546446874380218…80610616082494829441
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
1.117 Γ— 10⁹⁴(95-digit number)
11177546446874380218…80610616082494829441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.235 Γ— 10⁹⁴(95-digit number)
22355092893748760437…61221232164989658881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.471 Γ— 10⁹⁴(95-digit number)
44710185787497520875…22442464329979317761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.942 Γ— 10⁹⁴(95-digit number)
89420371574995041751…44884928659958635521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.788 Γ— 10⁹⁡(96-digit number)
17884074314999008350…89769857319917271041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.576 Γ— 10⁹⁡(96-digit number)
35768148629998016700…79539714639834542081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.153 Γ— 10⁹⁡(96-digit number)
71536297259996033401…59079429279669084161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.430 Γ— 10⁹⁢(97-digit number)
14307259451999206680…18158858559338168321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.861 Γ— 10⁹⁢(97-digit number)
28614518903998413360…36317717118676336641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.722 Γ— 10⁹⁢(97-digit number)
57229037807996826721…72635434237352673281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.144 Γ— 10⁹⁷(98-digit number)
11445807561599365344…45270868474705346561
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:57,755,814 XPMΒ·at block #6,813,966 Β· updates every 60s
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