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Block #2,619,552

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/18/2018, 1:08:45 PM Β· Difficulty 11.2483 Β· 4,197,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b3663f38241c45dd8d20b0bf6eda446abe7f789d485021076db8325330755a2d
View on Chainz β†—

Height

#2,619,552

Difficulty

11.248336

Transactions

2

Size

95.34 KB

Version

2

Bits

0b3f92ef

Nonce

1,480,871,603

Timestamp

4/18/2018, 1:08:45 PM

Confirmations

4,197,166

Mined by

⛏️ P2SHAQQtZ81JwhuL5VTqPz7feCJikE3ZM3T7Xd

Merkle Root

1f3bf07cba9160937f5808cc2c7cb1609b205742aef7d38cec51a4cee780e5af
Transactions (2)
Coinbase6e5429e3606dbc…59a72ef351864e
1 in β†’ 1 out8.8700 XPM109 B
AQQtZ81J…3ZM3T7Xd
4bce1d1f067814…9c91917ae01907
658 in β†’ 2 out400.0100 XPM95.14 KB
AXVhMzxC…yN7TDyJPALPF8J52…Hjw4BMsG
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.

3.910 Γ— 10⁹³(94-digit number)
39104146748007252672…82698419041019247999
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
3.910 Γ— 10⁹³(94-digit number)
39104146748007252672…82698419041019247999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.820 Γ— 10⁹³(94-digit number)
78208293496014505345…65396838082038495999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.564 Γ— 10⁹⁴(95-digit number)
15641658699202901069…30793676164076991999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.128 Γ— 10⁹⁴(95-digit number)
31283317398405802138…61587352328153983999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.256 Γ— 10⁹⁴(95-digit number)
62566634796811604276…23174704656307967999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.251 Γ— 10⁹⁡(96-digit number)
12513326959362320855…46349409312615935999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.502 Γ— 10⁹⁡(96-digit number)
25026653918724641710…92698818625231871999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.005 Γ— 10⁹⁡(96-digit number)
50053307837449283421…85397637250463743999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.001 Γ— 10⁹⁢(97-digit number)
10010661567489856684…70795274500927487999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.002 Γ— 10⁹⁢(97-digit number)
20021323134979713368…41590549001854975999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.004 Γ— 10⁹⁢(97-digit number)
40042646269959426737…83181098003709951999
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:57,777,868 XPMΒ·at block #6,816,717 Β· updates every 60s
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