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Block #2,051,549

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 1:32:47 PM Β· Difficulty 10.7175 Β· 4,789,824 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96f809e663c1c6750dbe466ff5424caa565ed82f2aaa9698ca4a9fde117d86b4
View on Chainz β†—

Height

#2,051,549

Difficulty

10.717534

Transactions

1

Size

199 B

Version

2

Bits

0ab7b04f

Nonce

103,104,541

Timestamp

4/3/2017, 1:32:47 PM

Confirmations

4,789,824

Mined by

⛏️ P2SHAWGPpcZjKgS4VEWZLVWh8jcHBJwXRA3j5i

Merkle Root

b26c92aa8f45164a26de5550baf80055464ca741ad4454c9c4cceb3867eafa51
Transactions (1)
Coinbaseb26c92aa8f4516…cceb3867eafa51
1 in β†’ 1 out8.6900 XPM109 B
AWGPpcZj…wXRA3j5i
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.

1.190 Γ— 10⁹⁡(96-digit number)
11908348183777250328…45131519761323082359
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
1.190 Γ— 10⁹⁡(96-digit number)
11908348183777250328…45131519761323082359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.381 Γ— 10⁹⁡(96-digit number)
23816696367554500656…90263039522646164719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.763 Γ— 10⁹⁡(96-digit number)
47633392735109001313…80526079045292329439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.526 Γ— 10⁹⁡(96-digit number)
95266785470218002627…61052158090584658879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.905 Γ— 10⁹⁢(97-digit number)
19053357094043600525…22104316181169317759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.810 Γ— 10⁹⁢(97-digit number)
38106714188087201050…44208632362338635519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.621 Γ— 10⁹⁢(97-digit number)
76213428376174402101…88417264724677271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.524 Γ— 10⁹⁷(98-digit number)
15242685675234880420…76834529449354542079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.048 Γ— 10⁹⁷(98-digit number)
30485371350469760840…53669058898709084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.097 Γ— 10⁹⁷(98-digit number)
60970742700939521681…07338117797418168319
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:57,975,355 XPMΒ·at block #6,841,372 Β· updates every 60s
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