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Block #2,684,250

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/30/2018, 9:18:19 AM Β· Difficulty 11.6909 Β· 4,146,870 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7fd9f1b2c8dde130a8ea3794c1d6e22d9f30d9e25d889d3c6383a9affd353dc2
View on Chainz β†—

Height

#2,684,250

Difficulty

11.690885

Transactions

2

Size

870 B

Version

2

Bits

0bb0dddc

Nonce

628,603,409

Timestamp

5/30/2018, 9:18:19 AM

Confirmations

4,146,870

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

1401a566c378c8bbcb602e4cae7dbd341114da33bac5f9a14bf6595e74b07f8c
Transactions (2)
Coinbase064f70b677fec3…849277cdedc8c3
1 in β†’ 1 out7.3100 XPM110 B
Adqah8zh…1WwoHJ9t
42f63ee674f2fa…ef6f48ff237123
4 in β†’ 2 out1250.0101 XPM669 B
AX3d5HGE…5KZcCuo2ALA3sZZW…zMR3MaSf
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.

2.572 Γ— 10⁹⁢(97-digit number)
25729628288376944067…17815746211035982079
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
2.572 Γ— 10⁹⁢(97-digit number)
25729628288376944067…17815746211035982079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.145 Γ— 10⁹⁢(97-digit number)
51459256576753888134…35631492422071964159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.029 Γ— 10⁹⁷(98-digit number)
10291851315350777626…71262984844143928319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.058 Γ— 10⁹⁷(98-digit number)
20583702630701555253…42525969688287856639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.116 Γ— 10⁹⁷(98-digit number)
41167405261403110507…85051939376575713279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.233 Γ— 10⁹⁷(98-digit number)
82334810522806221015…70103878753151426559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.646 Γ— 10⁹⁸(99-digit number)
16466962104561244203…40207757506302853119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.293 Γ— 10⁹⁸(99-digit number)
32933924209122488406…80415515012605706239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.586 Γ— 10⁹⁸(99-digit number)
65867848418244976812…60831030025211412479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.317 Γ— 10⁹⁹(100-digit number)
13173569683648995362…21662060050422824959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.634 Γ— 10⁹⁹(100-digit number)
26347139367297990724…43324120100845649919
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:57,893,106 XPMΒ·at block #6,831,119 Β· updates every 60s
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