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Block #2,216,002

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/21/2017, 8:09:56 AM Β· Difficulty 10.9435 Β· 4,611,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e10fd38cfa874a10c33cedcf6cc99922e03ef53fbeeafd103dd3bc7edad5a4a2
View on Chainz β†—

Height

#2,216,002

Difficulty

10.943508

Transactions

2

Size

7.47 KB

Version

2

Bits

0af189bb

Nonce

675,874,918

Timestamp

7/21/2017, 8:09:56 AM

Confirmations

4,611,303

Mined by

⛏️ P2SHARzV5utm6k4GAC3fgzi1tyJxhC8tNua8Y8

Merkle Root

bdc3cec8709f014a7dab72b330ff9479c6124fea29f637bf4728fa73723b8ece
Transactions (2)
Coinbasefc7bf47eebf6be…7c6934f94a9b93
1 in β†’ 1 out8.4200 XPM110 B
ARzV5utm…8tNua8Y8
3609c22c4155e3…b6a14ad56d2c04
50 in β†’ 1 out15698.6494 XPM7.27 KB
ANi9iofA…xijXWER2
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.

7.662 Γ— 10⁹⁡(96-digit number)
76623484956533726109…33308833353340991999
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
7.662 Γ— 10⁹⁡(96-digit number)
76623484956533726109…33308833353340991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.532 Γ— 10⁹⁢(97-digit number)
15324696991306745221…66617666706681983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.064 Γ— 10⁹⁢(97-digit number)
30649393982613490443…33235333413363967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.129 Γ— 10⁹⁢(97-digit number)
61298787965226980887…66470666826727935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.225 Γ— 10⁹⁷(98-digit number)
12259757593045396177…32941333653455871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.451 Γ— 10⁹⁷(98-digit number)
24519515186090792355…65882667306911743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.903 Γ— 10⁹⁷(98-digit number)
49039030372181584710…31765334613823487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.807 Γ— 10⁹⁷(98-digit number)
98078060744363169420…63530669227646975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.961 Γ— 10⁹⁸(99-digit number)
19615612148872633884…27061338455293951999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.923 Γ— 10⁹⁸(99-digit number)
39231224297745267768…54122676910587903999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.846 Γ— 10⁹⁸(99-digit number)
78462448595490535536…08245353821175807999
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:57,862,551 XPMΒ·at block #6,827,304 Β· updates every 60s
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