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Block #428,901

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/4/2014, 10:33:50 AM Β· Difficulty 10.3432 Β· 6,413,125 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5636c314c1680f29e5ccd876d720c01c2104948649562a1c2bc4858762383caa
View on Chainz β†—

Height

#428,901

Difficulty

10.343203

Transactions

2

Size

392 B

Version

2

Bits

0a57dc2e

Nonce

61,951,376

Timestamp

3/4/2014, 10:33:50 AM

Confirmations

6,413,125

Mined by

⛏️ P2SHAZ627nUzR2Dmg44G18DCeEPTereNcpQvnw

Merkle Root

137b7c18dc76da77ae9053107c6255508c32c504700a9445b2ba2f1b6cee991f
Transactions (2)
Coinbase135be7cb2e50e9…5440896f0f9ce6
1 in β†’ 1 out9.3404 XPM109 B
AZ627nUz…eNcpQvnw
55b2a84bc35518…a42c38c2ad6855
1 in β†’ 1 out2.9900 XPM192 B
AUdovToy…8v1QUdWv
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.

5.909 Γ— 10⁹⁡(96-digit number)
59090481652163920861…16550913762902506559
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
5.909 Γ— 10⁹⁡(96-digit number)
59090481652163920861…16550913762902506559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.181 Γ— 10⁹⁢(97-digit number)
11818096330432784172…33101827525805013119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.363 Γ— 10⁹⁢(97-digit number)
23636192660865568344…66203655051610026239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.727 Γ— 10⁹⁢(97-digit number)
47272385321731136688…32407310103220052479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.454 Γ— 10⁹⁢(97-digit number)
94544770643462273377…64814620206440104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.890 Γ— 10⁹⁷(98-digit number)
18908954128692454675…29629240412880209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.781 Γ— 10⁹⁷(98-digit number)
37817908257384909351…59258480825760419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.563 Γ— 10⁹⁷(98-digit number)
75635816514769818702…18516961651520839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁸(99-digit number)
15127163302953963740…37033923303041679359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.025 Γ— 10⁹⁸(99-digit number)
30254326605907927480…74067846606083358719
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:57,980,594 XPMΒ·at block #6,842,025 Β· updates every 60s
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