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Block #1,610,947

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/2/2016, 12:31:38 PM Β· Difficulty 10.6050 Β· 5,231,162 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c26f275473bac7d1b4139f651cac3e84dea1113aba728759b182297608c4f62a
View on Chainz β†—

Height

#1,610,947

Difficulty

10.604999

Transactions

1

Size

199 B

Version

2

Bits

0a9ae136

Nonce

224,517,727

Timestamp

6/2/2016, 12:31:38 PM

Confirmations

5,231,162

Mined by

⛏️ P2SHAPwH1b5x3qtAf9xfAqdd2zPeRGN2zKzEws

Merkle Root

a43c504fda3f97672bad4159b907a1f44a3f5ac133e886c973ddf6f5d1360c64
Transactions (1)
Coinbasea43c504fda3f97…ddf6f5d1360c64
1 in β†’ 1 out8.8800 XPM109 B
APwH1b5x…N2zKzEws
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.

8.003 Γ— 10⁹⁴(95-digit number)
80037538265441117545…93100895278580315519
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
8.003 Γ— 10⁹⁴(95-digit number)
80037538265441117545…93100895278580315519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.600 Γ— 10⁹⁡(96-digit number)
16007507653088223509…86201790557160631039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.201 Γ— 10⁹⁡(96-digit number)
32015015306176447018…72403581114321262079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.403 Γ— 10⁹⁡(96-digit number)
64030030612352894036…44807162228642524159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.280 Γ— 10⁹⁢(97-digit number)
12806006122470578807…89614324457285048319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.561 Γ— 10⁹⁢(97-digit number)
25612012244941157614…79228648914570096639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.122 Γ— 10⁹⁢(97-digit number)
51224024489882315229…58457297829140193279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.024 Γ— 10⁹⁷(98-digit number)
10244804897976463045…16914595658280386559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.048 Γ— 10⁹⁷(98-digit number)
20489609795952926091…33829191316560773119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.097 Γ— 10⁹⁷(98-digit number)
40979219591905852183…67658382633121546239
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:57,981,260 XPMΒ·at block #6,842,108 Β· updates every 60s
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