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Block #491,515

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/14/2014, 1:46:35 PM Β· Difficulty 10.6814 Β· 6,307,272 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
36e4901fa476a4f4f087112a01593d1f06e118307edd3fcbb6e8b42ce93c6b34
View on Chainz β†—

Height

#491,515

Difficulty

10.681357

Transactions

2

Size

543 B

Version

2

Bits

0aae6d6c

Nonce

44,370,244

Timestamp

4/14/2014, 1:46:35 PM

Confirmations

6,307,272

Mined by

⛏️ P2SHAaEVSQ9R1gCjU5Jk4SVVkYp1NcvEQ7wppQ

Merkle Root

af60c10169ecec2c2cf761a1fb18ffcbfd442583add162dd61f08269271713aa
Transactions (2)
Coinbasea2524c4df0b8e6…2abb6e6a380409
1 in β†’ 1 out8.7600 XPM112 B
AaEVSQ9R…vEQ7wppQ
34bfdf53ed09cf…09640fe1375160
2 in β†’ 1 out6.2721 XPM340 B
AZRPEac7…ixJb2qTx
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.

2.282 Γ— 10⁹⁷(98-digit number)
22827048535276733607…71701111462333637039
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
2.282 Γ— 10⁹⁷(98-digit number)
22827048535276733607…71701111462333637039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.565 Γ— 10⁹⁷(98-digit number)
45654097070553467214…43402222924667274079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.130 Γ— 10⁹⁷(98-digit number)
91308194141106934429…86804445849334548159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.826 Γ— 10⁹⁸(99-digit number)
18261638828221386885…73608891698669096319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.652 Γ— 10⁹⁸(99-digit number)
36523277656442773771…47217783397338192639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.304 Γ— 10⁹⁸(99-digit number)
73046555312885547543…94435566794676385279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.460 Γ— 10⁹⁹(100-digit number)
14609311062577109508…88871133589352770559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.921 Γ— 10⁹⁹(100-digit number)
29218622125154219017…77742267178705541119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.843 Γ— 10⁹⁹(100-digit number)
58437244250308438034…55484534357411082239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.168 Γ— 10¹⁰⁰(101-digit number)
11687448850061687606…10969068714822164479
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:57,634,327 XPMΒ·at block #6,798,786 Β· updates every 60s
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