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Block #507,396

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/23/2014, 5:19:46 PM Β· Difficulty 10.8159 Β· 6,298,672 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
526f71c3340c368e7bfaff578477bb2acd88a9fefe85435ed01075f56f0db029
View on Chainz β†—

Height

#507,396

Difficulty

10.815909

Transactions

2

Size

418 B

Version

2

Bits

0ad0df62

Nonce

233,351

Timestamp

4/23/2014, 5:19:46 PM

Confirmations

6,298,672

Mined by

⛏️ P2SHASXb8Msj7tnyLvWQxYzaaZ1YewBxGf64iZ

Merkle Root

545c98af47567b7987898b43263f3e083fcd114cd10df29c1a166e8652c7a45d
Transactions (2)
Coinbase96be0b6d497fd7…5f028d0746bfc4
1 in β†’ 1 out8.5400 XPM102 B
ASXb8Msj…BxGf64iZ
0b4bda4b95cc6d…9b000a8e31f164
1 in β†’ 2 out340.5000 XPM225 B
AUyUaUu7…6HHcSJQxAGndrCPx…72yKLrf8
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.

7.247 Γ— 10⁹⁡(96-digit number)
72475330737314559298…95494107997144166279
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
7.247 Γ— 10⁹⁡(96-digit number)
72475330737314559298…95494107997144166279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁢(97-digit number)
14495066147462911859…90988215994288332559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.899 Γ— 10⁹⁢(97-digit number)
28990132294925823719…81976431988576665119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.798 Γ— 10⁹⁢(97-digit number)
57980264589851647439…63952863977153330239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁷(98-digit number)
11596052917970329487…27905727954306660479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.319 Γ— 10⁹⁷(98-digit number)
23192105835940658975…55811455908613320959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.638 Γ— 10⁹⁷(98-digit number)
46384211671881317951…11622911817226641919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.276 Γ— 10⁹⁷(98-digit number)
92768423343762635902…23245823634453283839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.855 Γ— 10⁹⁸(99-digit number)
18553684668752527180…46491647268906567679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.710 Γ— 10⁹⁸(99-digit number)
37107369337505054361…92983294537813135359
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:57,692,623 XPMΒ·at block #6,806,067 Β· updates every 60s
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