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Block #2,781,682

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/6/2018, 12:29:32 PM Β· Difficulty 11.6497 Β· 4,052,298 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9d2c18e69bdef376f44ec1dccf2b0dd340ed4e540ed9e01aed521afedcbe021d
View on Chainz β†—

Height

#2,781,682

Difficulty

11.649702

Transactions

2

Size

19.92 KB

Version

2

Bits

0ba652e1

Nonce

120,004,772

Timestamp

8/6/2018, 12:29:32 PM

Confirmations

4,052,298

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

522989e376c0d707c78317d9ec8724bbba565da11b0114e37002e7d49f43b893
Transactions (2)
Coinbase54ca94f632915b…58d1e76a91df40
1 in β†’ 1 out7.5700 XPM110 B
AZtxQr2F…7grUWrUz
14c025dd1e1ac0…ec9fc4306dc51c
136 in β†’ 2 out3000.0100 XPM19.73 KB
AHk6UVth…sBKiDDzbAJ8jqSD5…JTPBK36z
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.

4.510 Γ— 10⁹⁴(95-digit number)
45109605857860884539…22643873812354928619
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
4.510 Γ— 10⁹⁴(95-digit number)
45109605857860884539…22643873812354928619
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.021 Γ— 10⁹⁴(95-digit number)
90219211715721769079…45287747624709857239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.804 Γ— 10⁹⁡(96-digit number)
18043842343144353815…90575495249419714479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.608 Γ— 10⁹⁡(96-digit number)
36087684686288707631…81150990498839428959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.217 Γ— 10⁹⁡(96-digit number)
72175369372577415263…62301980997678857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.443 Γ— 10⁹⁢(97-digit number)
14435073874515483052…24603961995357715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.887 Γ— 10⁹⁢(97-digit number)
28870147749030966105…49207923990715431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.774 Γ— 10⁹⁢(97-digit number)
57740295498061932210…98415847981430863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.154 Γ— 10⁹⁷(98-digit number)
11548059099612386442…96831695962861726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.309 Γ— 10⁹⁷(98-digit number)
23096118199224772884…93663391925723453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.619 Γ— 10⁹⁷(98-digit number)
46192236398449545768…87326783851446906879
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:57,916,065 XPMΒ·at block #6,833,979 Β· updates every 60s
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