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Block #2,133,323

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/26/2017, 10:37:24 AM Β· Difficulty 10.9097 Β· 4,708,211 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7f84d988f699e95776c03beb19b8f4ce8d074ba1097f20db6b2945cb1bfff4c4
View on Chainz β†—

Height

#2,133,323

Difficulty

10.909676

Transactions

2

Size

720 B

Version

2

Bits

0ae8e089

Nonce

658,360,623

Timestamp

5/26/2017, 10:37:24 AM

Confirmations

4,708,211

Mined by

⛏️ P2SHAcZBLiy84CW1jWncaqaxYhapyZ7Fc5QHtD

Merkle Root

2a27ed7c5998768d9527c95ff7096a16436d9b6ab301dd58374ca2f11039f2c6
Transactions (2)
Coinbasef9be284a2f56ee…5474387466a66d
1 in β†’ 1 out8.4000 XPM109 B
AcZBLiy8…7Fc5QHtD
8ebce7544dc6e8…986ca5cd37c65c
3 in β†’ 2 out281.0785 XPM522 B
AXXLKZ54…ZB6dGYfkAendE4DA…KywjAZcg
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.

8.916 Γ— 10⁹²(93-digit number)
89161164692047087436…73114744915847177799
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
8.916 Γ— 10⁹²(93-digit number)
89161164692047087436…73114744915847177799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.783 Γ— 10⁹³(94-digit number)
17832232938409417487…46229489831694355599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.566 Γ— 10⁹³(94-digit number)
35664465876818834974…92458979663388711199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.132 Γ— 10⁹³(94-digit number)
71328931753637669949…84917959326777422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.426 Γ— 10⁹⁴(95-digit number)
14265786350727533989…69835918653554844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.853 Γ— 10⁹⁴(95-digit number)
28531572701455067979…39671837307109689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.706 Γ— 10⁹⁴(95-digit number)
57063145402910135959…79343674614219379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.141 Γ— 10⁹⁡(96-digit number)
11412629080582027191…58687349228438758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.282 Γ— 10⁹⁡(96-digit number)
22825258161164054383…17374698456877516799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.565 Γ— 10⁹⁡(96-digit number)
45650516322328108767…34749396913755033599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.130 Γ— 10⁹⁡(96-digit number)
91301032644656217534…69498793827510067199
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,976,655 XPMΒ·at block #6,841,533 Β· updates every 60s
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