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Block #2,216,419

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2017, 3:38:39 PM Β· Difficulty 10.9431 Β· 4,610,140 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b28809599b1c55f80a1f7053aa8e9c586585964c7631bdccb4139288fe203ef
View on Chainz β†—

Height

#2,216,419

Difficulty

10.943148

Transactions

2

Size

868 B

Version

2

Bits

0af1722c

Nonce

170,016,199

Timestamp

7/21/2017, 3:38:39 PM

Confirmations

4,610,140

Mined by

⛏️ P2SHAbrj4J7LZ2iPUUAqaC9oeLvo9sRnoCT1Eo

Merkle Root

6432032aaa07dce499e80a1607da69ea3209bd9b2a495b690096cf350014cc3e
Transactions (2)
Coinbase0d044c7d9c15d8…d2f120ab7fafcc
1 in β†’ 1 out8.3500 XPM110 B
Abrj4J7L…RnoCT1Eo
6f264eb58ff990…a4501fdb860da0
4 in β†’ 2 out1349.4854 XPM668 B
AbCceF2S…DJkG35aUAdLv38Pf…k1z3e6Dc
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.

1.430 Γ— 10⁹⁴(95-digit number)
14307252210256513557…45226378953354503679
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
1.430 Γ— 10⁹⁴(95-digit number)
14307252210256513557…45226378953354503679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.861 Γ— 10⁹⁴(95-digit number)
28614504420513027114…90452757906709007359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.722 Γ— 10⁹⁴(95-digit number)
57229008841026054228…80905515813418014719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.144 Γ— 10⁹⁡(96-digit number)
11445801768205210845…61811031626836029439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.289 Γ— 10⁹⁡(96-digit number)
22891603536410421691…23622063253672058879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.578 Γ— 10⁹⁡(96-digit number)
45783207072820843382…47244126507344117759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.156 Γ— 10⁹⁡(96-digit number)
91566414145641686765…94488253014688235519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.831 Γ— 10⁹⁢(97-digit number)
18313282829128337353…88976506029376471039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.662 Γ— 10⁹⁢(97-digit number)
36626565658256674706…77953012058752942079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.325 Γ— 10⁹⁢(97-digit number)
73253131316513349412…55906024117505884159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.465 Γ— 10⁹⁷(98-digit number)
14650626263302669882…11812048235011768319
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:57,856,623 XPMΒ·at block #6,826,558 Β· updates every 60s
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