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Block #2,240,854

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2017, 10:55:22 AM Β· Difficulty 10.9465 Β· 4,586,314 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91fbcfefc655006b2db2dd7cf9a16f12168d5d43d8ebb6f72948b77e275ff239
View on Chainz β†—

Height

#2,240,854

Difficulty

10.946526

Transactions

2

Size

721 B

Version

2

Bits

0af24f86

Nonce

657,777,549

Timestamp

8/7/2017, 10:55:22 AM

Confirmations

4,586,314

Mined by

⛏️ P2SHASYFq4gLPP4JMjrwEwaMq2VGW95qXj2zhU

Merkle Root

0f3f7cda2f1f7cbc6f9e3b4395c21c37a3d372920694fed6450f94200dc275e4
Transactions (2)
Coinbase248a641d118bb1…b580998397054b
1 in β†’ 1 out8.3500 XPM109 B
ASYFq4gL…5qXj2zhU
3b7187e133eee4…4974fcf2b2ecaf
3 in β†’ 2 out163.4599 XPM522 B
Ad27Nz4m…CCnTdvs6ATGC2rkb…k6WiJya5
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.

2.075 Γ— 10⁹⁡(96-digit number)
20754515268857638833…70168186935691485119
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
2.075 Γ— 10⁹⁡(96-digit number)
20754515268857638833…70168186935691485119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.150 Γ— 10⁹⁡(96-digit number)
41509030537715277667…40336373871382970239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.301 Γ— 10⁹⁡(96-digit number)
83018061075430555334…80672747742765940479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁢(97-digit number)
16603612215086111066…61345495485531880959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.320 Γ— 10⁹⁢(97-digit number)
33207224430172222133…22690990971063761919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.641 Γ— 10⁹⁢(97-digit number)
66414448860344444267…45381981942127523839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.328 Γ— 10⁹⁷(98-digit number)
13282889772068888853…90763963884255047679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.656 Γ— 10⁹⁷(98-digit number)
26565779544137777707…81527927768510095359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.313 Γ— 10⁹⁷(98-digit number)
53131559088275555414…63055855537020190719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.062 Γ— 10⁹⁸(99-digit number)
10626311817655111082…26111711074040381439
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:57,861,440 XPMΒ·at block #6,827,167 Β· updates every 60s
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