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Block #2,173,708

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/23/2017, 12:36:31 PM Β· Difficulty 10.9098 Β· 4,668,592 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1bd00e963c75204cd75d175f90f2640ed65562fe585a8a680949704c8ef5eab0
View on Chainz β†—

Height

#2,173,708

Difficulty

10.909792

Transactions

1

Size

200 B

Version

2

Bits

0ae8e820

Nonce

1,706,013,927

Timestamp

6/23/2017, 12:36:31 PM

Confirmations

4,668,592

Mined by

⛏️ P2SHAdtjJSRMzvVbAFUfVwvcS6HezhtwmeSSCK

Merkle Root

59161494c73ea68c47251c95ce4ce4a490005561f2b1a44ec7b2db13bad9969d
Transactions (1)
Coinbase59161494c73ea6…b2db13bad9969d
1 in β†’ 1 out8.3900 XPM110 B
AdtjJSRM…twmeSSCK
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.

1.046 Γ— 10⁹⁡(96-digit number)
10469660349313754396…79952275814394640479
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
1.046 Γ— 10⁹⁡(96-digit number)
10469660349313754396…79952275814394640479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.093 Γ— 10⁹⁡(96-digit number)
20939320698627508792…59904551628789280959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.187 Γ— 10⁹⁡(96-digit number)
41878641397255017585…19809103257578561919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.375 Γ— 10⁹⁡(96-digit number)
83757282794510035171…39618206515157123839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.675 Γ— 10⁹⁢(97-digit number)
16751456558902007034…79236413030314247679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.350 Γ— 10⁹⁢(97-digit number)
33502913117804014068…58472826060628495359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.700 Γ— 10⁹⁢(97-digit number)
67005826235608028136…16945652121256990719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.340 Γ— 10⁹⁷(98-digit number)
13401165247121605627…33891304242513981439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.680 Γ— 10⁹⁷(98-digit number)
26802330494243211254…67782608485027962879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.360 Γ— 10⁹⁷(98-digit number)
53604660988486422509…35565216970055925759
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:57,982,804 XPMΒ·at block #6,842,299 Β· updates every 60s
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