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Block #455,806

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/22/2014, 6:55:06 PM Β· Difficulty 10.4167 Β· 6,339,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e9a557dc44ee72b2294448a36f117b4e5f98ba15ffb8a7c307de02497e508e0
View on Chainz β†—

Height

#455,806

Difficulty

10.416735

Transactions

2

Size

391 B

Version

2

Bits

0a6aaf2a

Nonce

21,944

Timestamp

3/22/2014, 6:55:06 PM

Confirmations

6,339,196

Mined by

⛏️ P2SHATbN2fgLeubaT3jjKLjxhXWqE5mY2ZknMy

Merkle Root

46769e186dd0b50d0178f30b2c92e9a1b646ae344ffbdfd7c31fbc962573fac5
Transactions (2)
Coinbasef76778aa801d63…e372e9079cbefd
1 in β†’ 1 out9.2100 XPM109 B
ATbN2fgL…mY2ZknMy
f756a743100c0a…5bb9cd4b900871
1 in β†’ 1 out9.9900 XPM191 B
AGirHFDM…vM2AgM21
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.

1.450 Γ— 10⁹⁷(98-digit number)
14507299177090519296…54215864188386463639
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
1.450 Γ— 10⁹⁷(98-digit number)
14507299177090519296…54215864188386463639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.901 Γ— 10⁹⁷(98-digit number)
29014598354181038593…08431728376772927279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.802 Γ— 10⁹⁷(98-digit number)
58029196708362077186…16863456753545854559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.160 Γ— 10⁹⁸(99-digit number)
11605839341672415437…33726913507091709119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.321 Γ— 10⁹⁸(99-digit number)
23211678683344830874…67453827014183418239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.642 Γ— 10⁹⁸(99-digit number)
46423357366689661749…34907654028366836479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.284 Γ— 10⁹⁸(99-digit number)
92846714733379323498…69815308056733672959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.856 Γ— 10⁹⁹(100-digit number)
18569342946675864699…39630616113467345919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.713 Γ— 10⁹⁹(100-digit number)
37138685893351729399…79261232226934691839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.427 Γ— 10⁹⁹(100-digit number)
74277371786703458799…58522464453869383679
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:57,604,059 XPMΒ·at block #6,795,001 Β· updates every 60s
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