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Block #2,268,870

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/26/2017, 1:01:16 PM Β· Difficulty 10.9527 Β· 4,572,911 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c0b590859153bdb576e66a885534fcf85fe1f8cbee7bc5d554d95004e9fd65cd
View on Chainz β†—

Height

#2,268,870

Difficulty

10.952693

Transactions

2

Size

1020 B

Version

2

Bits

0af3e3b3

Nonce

878,921,217

Timestamp

8/26/2017, 1:01:16 PM

Confirmations

4,572,911

Mined by

⛏️ P2SHAHs6prVs2kTQHJtG3NGB3AU88uPAsqZ9mE

Merkle Root

30efab08906b4f11ff462119e4cec7afaa870376761c57a3569e235cfa7702b9
Transactions (2)
Coinbase77fc5cfaa29be6…21d19fccf3fe64
1 in β†’ 1 out8.3300 XPM110 B
AHs6prVs…PAsqZ9mE
c4f1dae1faf010…348d100250add1
5 in β†’ 2 out1142.5104 XPM819 B
ALfb3AgN…gyt3DNb1AZJXs5PE…3zVUDSdL
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.

1.294 Γ— 10⁹⁢(97-digit number)
12942547501301900690…89406327126173183999
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
1.294 Γ— 10⁹⁢(97-digit number)
12942547501301900690…89406327126173183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.588 Γ— 10⁹⁢(97-digit number)
25885095002603801381…78812654252346367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.177 Γ— 10⁹⁢(97-digit number)
51770190005207602763…57625308504692735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.035 Γ— 10⁹⁷(98-digit number)
10354038001041520552…15250617009385471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.070 Γ— 10⁹⁷(98-digit number)
20708076002083041105…30501234018770943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.141 Γ— 10⁹⁷(98-digit number)
41416152004166082210…61002468037541887999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.283 Γ— 10⁹⁷(98-digit number)
82832304008332164421…22004936075083775999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.656 Γ— 10⁹⁸(99-digit number)
16566460801666432884…44009872150167551999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.313 Γ— 10⁹⁸(99-digit number)
33132921603332865768…88019744300335103999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.626 Γ— 10⁹⁸(99-digit number)
66265843206665731537…76039488600670207999
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:57,978,625 XPMΒ·at block #6,841,780 Β· updates every 60s
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