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Block #2,103,765

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2017, 11:28:05 PM Β· Difficulty 10.8765 Β· 4,741,450 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3ceeec63801c89d62165cdbe9d951d70dc35c04916485518f7ffcdb8e2f3d284
View on Chainz β†—

Height

#2,103,765

Difficulty

10.876469

Transactions

2

Size

428 B

Version

2

Bits

0ae06049

Nonce

115,734,560

Timestamp

5/6/2017, 11:28:05 PM

Confirmations

4,741,450

Mined by

⛏️ P2SHAV1CaUXyMPSNSusrxqSiJGNkXoVDKCVMt7

Merkle Root

9e45e5b8fd681cdafcdc074eca2210beb39b95aa11d2d053b0138ec0eae267aa
Transactions (2)
Coinbase137dd69e9725c2…055b83fa1e4375
1 in β†’ 1 out8.4500 XPM110 B
AV1CaUXy…VDKCVMt7
aefa22ed31c3fa…a479a7dcabea5a
1 in β†’ 2 out1385.9900 XPM227 B
AUodLX3T…3Je1SfstAXoA1ovx…z5C8yaiu
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.

8.428 Γ— 10⁹⁢(97-digit number)
84286962919887142352…52781476387719854079
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
8.428 Γ— 10⁹⁢(97-digit number)
84286962919887142352…52781476387719854079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.685 Γ— 10⁹⁷(98-digit number)
16857392583977428470…05562952775439708159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.371 Γ— 10⁹⁷(98-digit number)
33714785167954856941…11125905550879416319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.742 Γ— 10⁹⁷(98-digit number)
67429570335909713882…22251811101758832639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.348 Γ— 10⁹⁸(99-digit number)
13485914067181942776…44503622203517665279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.697 Γ— 10⁹⁸(99-digit number)
26971828134363885552…89007244407035330559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.394 Γ— 10⁹⁸(99-digit number)
53943656268727771105…78014488814070661119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.078 Γ— 10⁹⁹(100-digit number)
10788731253745554221…56028977628141322239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.157 Γ— 10⁹⁹(100-digit number)
21577462507491108442…12057955256282644479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.315 Γ— 10⁹⁹(100-digit number)
43154925014982216884…24115910512565288959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.630 Γ— 10⁹⁹(100-digit number)
86309850029964433769…48231821025130577919
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:58,006,153 XPMΒ·at block #6,845,214 Β· updates every 60s
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