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Block #1,661,571

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/6/2016, 8:09:45 AM Β· Difficulty 10.7323 Β· 5,145,523 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ae012ac08960662b6423ca7528c734840f7c4f9f9b96a37d537ae94d13e4a3a9
View on Chainz β†—

Height

#1,661,571

Difficulty

10.732284

Transactions

2

Size

21.21 KB

Version

2

Bits

0abb76f9

Nonce

881,221,997

Timestamp

7/6/2016, 8:09:45 AM

Confirmations

5,145,523

Mined by

⛏️ P2SHAJ794c8vX6pg84ZxXwrCroXq2ZTyvQwT3P

Merkle Root

14033ff511dd99c8ee592253b5bbddca6da300dbfabaf8d13744d4f38ece75e0
Transactions (2)
Coinbase548ecfea5838a7…61e9d306d09b7f
1 in β†’ 1 out8.8900 XPM110 B
AJ794c8v…TyvQwT3P
76beea7697c76a…3f12785dc42e4c
145 in β†’ 2 out20.2914 XPM21.02 KB
AZ7FpdtV…ZA5S6avrAGyiGjWR…yy2Gk1HV
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.

4.252 Γ— 10⁹⁴(95-digit number)
42526529088688962707…24195839047854234319
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
4.252 Γ— 10⁹⁴(95-digit number)
42526529088688962707…24195839047854234319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.505 Γ— 10⁹⁴(95-digit number)
85053058177377925414…48391678095708468639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.701 Γ— 10⁹⁡(96-digit number)
17010611635475585082…96783356191416937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.402 Γ— 10⁹⁡(96-digit number)
34021223270951170165…93566712382833874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.804 Γ— 10⁹⁡(96-digit number)
68042446541902340331…87133424765667749119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.360 Γ— 10⁹⁢(97-digit number)
13608489308380468066…74266849531335498239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.721 Γ— 10⁹⁢(97-digit number)
27216978616760936132…48533699062670996479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.443 Γ— 10⁹⁢(97-digit number)
54433957233521872265…97067398125341992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.088 Γ— 10⁹⁷(98-digit number)
10886791446704374453…94134796250683985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.177 Γ— 10⁹⁷(98-digit number)
21773582893408748906…88269592501367971839
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:57,700,850 XPMΒ·at block #6,807,093 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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