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Block #2,698,982

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/10/2018, 2:26:16 AM Β· Difficulty 11.6457 Β· 4,144,979 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7e864390bcf15355a5628997c173579fbef71c95d6b3d47e3d138317f3a10e55
View on Chainz β†—

Height

#2,698,982

Difficulty

11.645745

Transactions

1

Size

201 B

Version

2

Bits

0ba54f84

Nonce

1,270,854,521

Timestamp

6/10/2018, 2:26:16 AM

Confirmations

4,144,979

Mined by

⛏️ P2SHALFdYteLEFGEjXtWHun43u7AcC9DpGxdu4

Merkle Root

5a1433ef7cadea8e3b0c822159a39c22fdba8f53fc66726fb5b90f5e51a0ae8c
Transactions (1)
Coinbase5a1433ef7cadea…b90f5e51a0ae8c
1 in β†’ 1 out7.3600 XPM110 B
ALFdYteL…9DpGxdu4
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.

1.300 Γ— 10⁹⁢(97-digit number)
13005987122846459518…22845410698734145279
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
1.300 Γ— 10⁹⁢(97-digit number)
13005987122846459518…22845410698734145279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.601 Γ— 10⁹⁢(97-digit number)
26011974245692919037…45690821397468290559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.202 Γ— 10⁹⁢(97-digit number)
52023948491385838075…91381642794936581119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.040 Γ— 10⁹⁷(98-digit number)
10404789698277167615…82763285589873162239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.080 Γ— 10⁹⁷(98-digit number)
20809579396554335230…65526571179746324479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.161 Γ— 10⁹⁷(98-digit number)
41619158793108670460…31053142359492648959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.323 Γ— 10⁹⁷(98-digit number)
83238317586217340920…62106284718985297919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.664 Γ— 10⁹⁸(99-digit number)
16647663517243468184…24212569437970595839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.329 Γ— 10⁹⁸(99-digit number)
33295327034486936368…48425138875941191679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.659 Γ— 10⁹⁸(99-digit number)
66590654068973872736…96850277751882383359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.331 Γ— 10⁹⁹(100-digit number)
13318130813794774547…93700555503764766719
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:57,996,065 XPMΒ·at block #6,843,960 Β· updates every 60s
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