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Block #507,572

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/23/2014, 8:03:29 PM Β· Difficulty 10.8164 Β· 6,288,051 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4f4de8f19841b9c276c763e0191c89c00372b4c3ce6dd0da9a5a7b116638be8d
View on Chainz β†—

Height

#507,572

Difficulty

10.816415

Transactions

2

Size

4.43 KB

Version

2

Bits

0ad10090

Nonce

15,850

Timestamp

4/23/2014, 8:03:29 PM

Confirmations

6,288,051

Mined by

⛏️ P2SHAG6bMm6XCYxTkS8dnRdQucikJa52K58LcR

Merkle Root

719c2ad949bbad849c1a1c9471a0a00f93d2f33bdcb21141fc9c1518005611e3
Transactions (2)
Coinbase12caa3ef419f03…84defe47921435
1 in β†’ 1 out8.5800 XPM111 B
AG6bMm6X…52K58LcR
4978f572816d39…cbc6ede6d44e57
29 in β†’ 1 out87.4846 XPM4.23 KB
AZVUR6Mi…kZZL2G8K
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.

6.961 Γ— 10⁹⁸(99-digit number)
69616838740686606018…50565320846690519319
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
6.961 Γ— 10⁹⁸(99-digit number)
69616838740686606018…50565320846690519319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.392 Γ— 10⁹⁹(100-digit number)
13923367748137321203…01130641693381038639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.784 Γ— 10⁹⁹(100-digit number)
27846735496274642407…02261283386762077279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.569 Γ— 10⁹⁹(100-digit number)
55693470992549284814…04522566773524154559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.113 Γ— 10¹⁰⁰(101-digit number)
11138694198509856962…09045133547048309119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.227 Γ— 10¹⁰⁰(101-digit number)
22277388397019713925…18090267094096618239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.455 Γ— 10¹⁰⁰(101-digit number)
44554776794039427851…36180534188193236479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.910 Γ— 10¹⁰⁰(101-digit number)
89109553588078855703…72361068376386472959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.782 Γ— 10¹⁰¹(102-digit number)
17821910717615771140…44722136752772945919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.564 Γ— 10¹⁰¹(102-digit number)
35643821435231542281…89444273505545891839
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:57,609,051 XPMΒ·at block #6,795,622 Β· updates every 60s
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