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Block #1,987,074

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/17/2017, 12:16:32 PM Β· Difficulty 10.7353 Β· 4,855,258 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7de7981ced0128544faece83bfbe096921423d09162b3d39b04f5fbe25727a52
View on Chainz β†—

Height

#1,987,074

Difficulty

10.735284

Transactions

2

Size

1.54 KB

Version

2

Bits

0abc3b8c

Nonce

198,163,244

Timestamp

2/17/2017, 12:16:32 PM

Confirmations

4,855,258

Mined by

⛏️ P2SHAH4TqZu9bTiczrAhJmociDXCrPvp8CDpJT

Merkle Root

ead397fc3f095153a87284ea430cbde3a2b56d11d4c24b20097c61db0feba460
Transactions (2)
Coinbase369d6f686691d9…65e02bbf2821fd
1 in β†’ 1 out8.6900 XPM109 B
AH4TqZu9…vp8CDpJT
36f0673a53852c…75b77c8c673995
9 in β†’ 1 out12760.0000 XPM1.34 KB
AYJCQHHj…bPaKNbHS
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.

1.836 Γ— 10⁹⁡(96-digit number)
18364404112052651609…31486159640306620479
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
1.836 Γ— 10⁹⁡(96-digit number)
18364404112052651609…31486159640306620479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.672 Γ— 10⁹⁡(96-digit number)
36728808224105303219…62972319280613240959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.345 Γ— 10⁹⁡(96-digit number)
73457616448210606439…25944638561226481919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.469 Γ— 10⁹⁢(97-digit number)
14691523289642121287…51889277122452963839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.938 Γ— 10⁹⁢(97-digit number)
29383046579284242575…03778554244905927679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.876 Γ— 10⁹⁢(97-digit number)
58766093158568485151…07557108489811855359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.175 Γ— 10⁹⁷(98-digit number)
11753218631713697030…15114216979623710719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.350 Γ— 10⁹⁷(98-digit number)
23506437263427394060…30228433959247421439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.701 Γ— 10⁹⁷(98-digit number)
47012874526854788121…60456867918494842879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.402 Γ— 10⁹⁷(98-digit number)
94025749053709576242…20913735836989685759
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:57,983,061 XPMΒ·at block #6,842,331 Β· updates every 60s
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