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Block #3,445,460

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/23/2019, 1:26:34 PM Β· Difficulty 10.9789 Β· 3,395,664 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4dc40f3a76837228bf3dfb66bc8fea54fbdfde27ee680f622f890a684f6a4238
View on Chainz β†—

Height

#3,445,460

Difficulty

10.978907

Transactions

2

Size

3.98 KB

Version

2

Bits

0afa99a8

Nonce

1,099,136,437

Timestamp

11/23/2019, 1:26:34 PM

Confirmations

3,395,664

Mined by

⛏️ P2SHASiq2qtKTzQ7sbERFE8Jp8HjsgVMhmk7yL

Merkle Root

03eddba9252052db3f3f6c6e88517a448269107b69b14430448ddd72942811c5
Transactions (2)
Coinbase70101da73908b1…1ef7a165da58c6
1 in β†’ 1 out8.3200 XPM110 B
ASiq2qtK…VMhmk7yL
8b21ad09a63292…0334aeead5e291
26 in β†’ 1 out260.9114 XPM3.79 KB
AXoSyMCe…Z8KXiWkn
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.

2.491 Γ— 10⁹³(94-digit number)
24918666883712594058…12284216073469945599
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
2.491 Γ— 10⁹³(94-digit number)
24918666883712594058…12284216073469945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.983 Γ— 10⁹³(94-digit number)
49837333767425188117…24568432146939891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.967 Γ— 10⁹³(94-digit number)
99674667534850376234…49136864293879782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.993 Γ— 10⁹⁴(95-digit number)
19934933506970075246…98273728587759564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.986 Γ— 10⁹⁴(95-digit number)
39869867013940150493…96547457175519129599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.973 Γ— 10⁹⁴(95-digit number)
79739734027880300987…93094914351038259199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.594 Γ— 10⁹⁡(96-digit number)
15947946805576060197…86189828702076518399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.189 Γ— 10⁹⁡(96-digit number)
31895893611152120394…72379657404153036799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.379 Γ— 10⁹⁡(96-digit number)
63791787222304240789…44759314808306073599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.275 Γ— 10⁹⁢(97-digit number)
12758357444460848157…89518629616612147199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.551 Γ— 10⁹⁢(97-digit number)
25516714888921696315…79037259233224294399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,973,361 XPMΒ·at block #6,841,123 Β· updates every 60s
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