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Block #2,051,550

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 1:33:04 PM Β· Difficulty 10.7176 Β· 4,788,526 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a057c3f3460164230e034deada7e940c9045c0c70014b1663700594d9fdaa7d7
View on Chainz β†—

Height

#2,051,550

Difficulty

10.717571

Transactions

1

Size

199 B

Version

2

Bits

0ab7b2c2

Nonce

8,557,032

Timestamp

4/3/2017, 1:33:04 PM

Confirmations

4,788,526

Mined by

⛏️ P2SHAX7aG26rsYTPWVPweHSJhL84KLVNHjZDq3

Merkle Root

7e421bbf6f088f1f8cd2dab3f70b86d38b345f3a845994433a6e99fd38fc2ebb
Transactions (1)
Coinbase7e421bbf6f088f…6e99fd38fc2ebb
1 in β†’ 1 out8.6900 XPM109 B
AX7aG26r…VNHjZDq3
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.

1.424 Γ— 10⁹⁴(95-digit number)
14242209251571877240…26124775800041653199
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
1.424 Γ— 10⁹⁴(95-digit number)
14242209251571877240…26124775800041653199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.848 Γ— 10⁹⁴(95-digit number)
28484418503143754480…52249551600083306399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.696 Γ— 10⁹⁴(95-digit number)
56968837006287508961…04499103200166612799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁡(96-digit number)
11393767401257501792…08998206400333225599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.278 Γ— 10⁹⁡(96-digit number)
22787534802515003584…17996412800666451199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.557 Γ— 10⁹⁡(96-digit number)
45575069605030007169…35992825601332902399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.115 Γ— 10⁹⁡(96-digit number)
91150139210060014338…71985651202665804799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.823 Γ— 10⁹⁢(97-digit number)
18230027842012002867…43971302405331609599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.646 Γ— 10⁹⁢(97-digit number)
36460055684024005735…87942604810663219199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.292 Γ— 10⁹⁢(97-digit number)
72920111368048011470…75885209621326438399
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,964,915 XPMΒ·at block #6,840,075 Β· updates every 60s
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