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Block #2,124,795

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/20/2017, 3:45:33 AM Β· Difficulty 10.9183 Β· 4,706,903 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f872f128e92d9c5bc580482a95a5b531798af7cef330c06a0415b6ee58ba75d
View on Chainz β†—

Height

#2,124,795

Difficulty

10.918330

Transactions

2

Size

1.10 KB

Version

2

Bits

0aeb17b3

Nonce

300,176,592

Timestamp

5/20/2017, 3:45:33 AM

Confirmations

4,706,903

Mined by

⛏️ P2SHAPcdES8nAJukrnTAPVZLcgxq9Y7N3MNoG8

Merkle Root

cddc57bdd2d2cf5e03e95419455495ca72623d819ab5bc3e94f802bc69d2b658
Transactions (2)
Coinbase5101552b48a427…972a639d00af2a
1 in β†’ 1 out8.4000 XPM110 B
APcdES8n…7N3MNoG8
3bafe67e89bc0a…9a41e5bc50ce6a
6 in β†’ 1 out100.8385 XPM931 B
Ab5hDQfj…dXyTSefZ
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.

5.969 Γ— 10⁹³(94-digit number)
59695987024500828560…27422999343287839479
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
5.969 Γ— 10⁹³(94-digit number)
59695987024500828560…27422999343287839479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.193 Γ— 10⁹⁴(95-digit number)
11939197404900165712…54845998686575678959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.387 Γ— 10⁹⁴(95-digit number)
23878394809800331424…09691997373151357919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.775 Γ— 10⁹⁴(95-digit number)
47756789619600662848…19383994746302715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.551 Γ— 10⁹⁴(95-digit number)
95513579239201325696…38767989492605431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.910 Γ— 10⁹⁡(96-digit number)
19102715847840265139…77535978985210863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.820 Γ— 10⁹⁡(96-digit number)
38205431695680530278…55071957970421726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.641 Γ— 10⁹⁡(96-digit number)
76410863391361060557…10143915940843453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.528 Γ— 10⁹⁢(97-digit number)
15282172678272212111…20287831881686906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.056 Γ— 10⁹⁢(97-digit number)
30564345356544424222…40575663763373813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.112 Γ— 10⁹⁢(97-digit number)
61128690713088848445…81151327526747627519
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:57,897,693 XPMΒ·at block #6,831,697 Β· updates every 60s
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