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Block #2,138,265

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/30/2017, 5:52:20 PM Β· Difficulty 10.8844 Β· 4,706,879 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
38ddcb8d207d1618be514eb60c3aa6f33b33ac6b51bcddf12c52a7b97b7b8d7c
View on Chainz β†—

Height

#2,138,265

Difficulty

10.884374

Transactions

2

Size

1017 B

Version

2

Bits

0ae26656

Nonce

705,219,764

Timestamp

5/30/2017, 5:52:20 PM

Confirmations

4,706,879

Mined by

⛏️ P2SHAPvXJbDTzctgHW4siMS5y4gFwM8VG7C15G

Merkle Root

b3b9af038ab765f390ba913dd45473c7e9cc8d056a9fae3967a54f1acdc9cb55
Transactions (2)
Coinbase79a6e66b227f5e…0c4d843a4c025b
1 in β†’ 1 out8.4400 XPM109 B
APvXJbDT…8VG7C15G
8a3add6581e196…fbe170a3b0d32a
5 in β†’ 2 out32.7335 XPM818 B
Acwu4RZs…G7NySiRrAd13QTN4…ddfdRmC1
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.

1.886 Γ— 10⁹⁡(96-digit number)
18869731824615331211…36047775482126038599
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
1.886 Γ— 10⁹⁡(96-digit number)
18869731824615331211…36047775482126038599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.773 Γ— 10⁹⁡(96-digit number)
37739463649230662422…72095550964252077199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.547 Γ— 10⁹⁡(96-digit number)
75478927298461324844…44191101928504154399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.509 Γ— 10⁹⁢(97-digit number)
15095785459692264968…88382203857008308799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.019 Γ— 10⁹⁢(97-digit number)
30191570919384529937…76764407714016617599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.038 Γ— 10⁹⁢(97-digit number)
60383141838769059875…53528815428033235199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.207 Γ— 10⁹⁷(98-digit number)
12076628367753811975…07057630856066470399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.415 Γ— 10⁹⁷(98-digit number)
24153256735507623950…14115261712132940799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.830 Γ— 10⁹⁷(98-digit number)
48306513471015247900…28230523424265881599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.661 Γ— 10⁹⁷(98-digit number)
96613026942030495800…56461046848531763199
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:58,005,580 XPMΒ·at block #6,845,143 Β· updates every 60s
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