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Block #364,633

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/18/2014, 5:08:42 AM Β· Difficulty 10.4214 Β· 6,447,526 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
de59edcfec0ac20dcefa19a06fbe4ef74a7fe3c83295b88fec7dfc5cbfe6c499
View on Chainz β†—

Height

#364,633

Difficulty

10.421422

Transactions

1

Size

207 B

Version

2

Bits

0a6be24c

Nonce

711,092

Timestamp

1/18/2014, 5:08:42 AM

Confirmations

6,447,526

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4688d8bb2300e94eb74a0b27db430febf61b74b171ef31993e2985a1e5d8bc77
Transactions (1)
Coinbase4688d8bb2300e9…2985a1e5d8bc77
1 in β†’ 1 out9.1900 XPM116 B
AbwWkWZt…kawDhufa
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.

3.964 Γ— 10⁹⁢(97-digit number)
39648966844986202783…73570334598503625519
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
3.964 Γ— 10⁹⁢(97-digit number)
39648966844986202783…73570334598503625519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.929 Γ— 10⁹⁢(97-digit number)
79297933689972405566…47140669197007251039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.585 Γ— 10⁹⁷(98-digit number)
15859586737994481113…94281338394014502079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.171 Γ— 10⁹⁷(98-digit number)
31719173475988962226…88562676788029004159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.343 Γ— 10⁹⁷(98-digit number)
63438346951977924453…77125353576058008319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.268 Γ— 10⁹⁸(99-digit number)
12687669390395584890…54250707152116016639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.537 Γ— 10⁹⁸(99-digit number)
25375338780791169781…08501414304232033279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.075 Γ— 10⁹⁸(99-digit number)
50750677561582339562…17002828608464066559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.015 Γ— 10⁹⁹(100-digit number)
10150135512316467912…34005657216928133119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.030 Γ— 10⁹⁹(100-digit number)
20300271024632935825…68011314433856266239
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:57,741,289 XPMΒ·at block #6,812,158 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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