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Block #373,659

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/24/2014, 11:36:45 AM Β· Difficulty 10.4240 Β· 6,432,738 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
db02d6c88a137fc936aea86fba80b8e3b99e13db16560b0303c7378a9734b149
View on Chainz β†—

Height

#373,659

Difficulty

10.424045

Transactions

2

Size

393 B

Version

2

Bits

0a6c8e37

Nonce

269,411

Timestamp

1/24/2014, 11:36:45 AM

Confirmations

6,432,738

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

64e9a8103c85ee68183d8d9b2c97e7a4b31d892528b6161dca29560aa504d813
Transactions (2)
Coinbasee80f44dc0e89cd…d68e28f74edcb1
1 in β†’ 1 out9.2006 XPM110 B
AeKNrjNj…1NEq95Ta
58e83a315eba40…4f6e47112a7469
1 in β†’ 1 out2.9900 XPM192 B
AUvmGj9D…fchFX8bk
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.

3.938 Γ— 10⁹⁢(97-digit number)
39387192566215433532…43696047272039921019
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
3.938 Γ— 10⁹⁢(97-digit number)
39387192566215433532…43696047272039921019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.877 Γ— 10⁹⁢(97-digit number)
78774385132430867064…87392094544079842039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.575 Γ— 10⁹⁷(98-digit number)
15754877026486173412…74784189088159684079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.150 Γ— 10⁹⁷(98-digit number)
31509754052972346825…49568378176319368159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.301 Γ— 10⁹⁷(98-digit number)
63019508105944693651…99136756352638736319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.260 Γ— 10⁹⁸(99-digit number)
12603901621188938730…98273512705277472639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.520 Γ— 10⁹⁸(99-digit number)
25207803242377877460…96547025410554945279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.041 Γ— 10⁹⁸(99-digit number)
50415606484755754921…93094050821109890559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.008 Γ— 10⁹⁹(100-digit number)
10083121296951150984…86188101642219781119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.016 Γ— 10⁹⁹(100-digit number)
20166242593902301968…72376203284439562239
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:57,695,268 XPMΒ·at block #6,806,396 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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