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Block #363,297

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2014, 8:06:11 AM Β· Difficulty 10.4119 Β· 6,444,907 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37bae990d3894ae473a823d366a15a47ea06ea910380acbfd1bad7b31f0f1925
View on Chainz β†—

Height

#363,297

Difficulty

10.411950

Transactions

2

Size

834 B

Version

2

Bits

0a69758c

Nonce

5,504

Timestamp

1/17/2014, 8:06:11 AM

Confirmations

6,444,907

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

862f035a9306deca6086d7912d1390677247c3ee12d5042ed43e0eadd82063c1
Transactions (2)
Coinbase0b4a36e4886c61…18d0d4340402de
1 in β†’ 1 out9.2200 XPM110 B
AeKNrjNj…1NEq95Ta
93fda7245f2980…bd21d9808636de
4 in β†’ 1 out8.5235 XPM635 B
APhZbt91…ERWP9zpq
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.

2.582 Γ— 10⁹³(94-digit number)
25820170344887859547…50237097612540691139
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
2.582 Γ— 10⁹³(94-digit number)
25820170344887859547…50237097612540691139
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.164 Γ— 10⁹³(94-digit number)
51640340689775719095…00474195225081382279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.032 Γ— 10⁹⁴(95-digit number)
10328068137955143819…00948390450162764559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.065 Γ— 10⁹⁴(95-digit number)
20656136275910287638…01896780900325529119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.131 Γ— 10⁹⁴(95-digit number)
41312272551820575276…03793561800651058239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.262 Γ— 10⁹⁴(95-digit number)
82624545103641150553…07587123601302116479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁡(96-digit number)
16524909020728230110…15174247202604232959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.304 Γ— 10⁹⁡(96-digit number)
33049818041456460221…30348494405208465919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.609 Γ— 10⁹⁡(96-digit number)
66099636082912920442…60696988810416931839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.321 Γ— 10⁹⁢(97-digit number)
13219927216582584088…21393977620833863679
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:57,709,684 XPMΒ·at block #6,808,203 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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