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Block #2,051,514

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 1:18:13 PM Β· Difficulty 10.7164 Β· 4,791,577 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd8ec9268b98f1a77ad89c9ab43eba6a52b3a65297f89a6c9affbe47f12223a7
View on Chainz β†—

Height

#2,051,514

Difficulty

10.716369

Transactions

1

Size

199 B

Version

2

Bits

0ab763f4

Nonce

285,804,334

Timestamp

4/3/2017, 1:18:13 PM

Confirmations

4,791,577

Mined by

⛏️ P2SHAQHxMfuNuYkSySuUQjvxf98e1kV6pLmuAH

Merkle Root

0961476c07e7fbb584acb5ae3b4c22eace1c019c779dce9cb7d34c1ebff194ac
Transactions (1)
Coinbase0961476c07e7fb…d34c1ebff194ac
1 in β†’ 1 out8.6900 XPM110 B
AQHxMfuN…V6pLmuAH
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.

1.536 Γ— 10⁹²(93-digit number)
15363555471486376765…96825253696554160999
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
1.536 Γ— 10⁹²(93-digit number)
15363555471486376765…96825253696554160999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.072 Γ— 10⁹²(93-digit number)
30727110942972753531…93650507393108321999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.145 Γ— 10⁹²(93-digit number)
61454221885945507062…87301014786216643999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.229 Γ— 10⁹³(94-digit number)
12290844377189101412…74602029572433287999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.458 Γ— 10⁹³(94-digit number)
24581688754378202824…49204059144866575999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.916 Γ— 10⁹³(94-digit number)
49163377508756405649…98408118289733151999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.832 Γ— 10⁹³(94-digit number)
98326755017512811299…96816236579466303999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.966 Γ— 10⁹⁴(95-digit number)
19665351003502562259…93632473158932607999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.933 Γ— 10⁹⁴(95-digit number)
39330702007005124519…87264946317865215999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.866 Γ— 10⁹⁴(95-digit number)
78661404014010249039…74529892635730431999
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:57,989,090 XPMΒ·at block #6,843,090 Β· updates every 60s
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