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Block #63,904

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/19/2013, 4:26:19 AM Β· Difficulty 8.9803 Β· 6,730,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f2fa45498c8cc7f2b335f7f86bbdba18620c647e150cb40dcd7b1815b7a95872
View on Chainz β†—

Height

#63,904

Difficulty

8.980342

Transactions

1

Size

200 B

Version

2

Bits

08faf7ab

Nonce

601

Timestamp

7/19/2013, 4:26:19 AM

Confirmations

6,730,498

Mined by

⛏️ P2SHAQEbmWMhm3AfNhyeGW1Fbr2Y8UbVPpCt5X

Merkle Root

05563a11ad1b93c2b2046a4a116ce3881429edaa36592216251fba346ebb98ed
Transactions (1)
Coinbase05563a11ad1b93…1fba346ebb98ed
1 in β†’ 1 out12.3800 XPM110 B
AQEbmWMh…bVPpCt5X
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.

7.634 Γ— 10⁹⁴(95-digit number)
76341440173549631522…12632188179970735919
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
7.634 Γ— 10⁹⁴(95-digit number)
76341440173549631522…12632188179970735919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.526 Γ— 10⁹⁡(96-digit number)
15268288034709926304…25264376359941471839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.053 Γ— 10⁹⁡(96-digit number)
30536576069419852609…50528752719882943679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.107 Γ— 10⁹⁡(96-digit number)
61073152138839705218…01057505439765887359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.221 Γ— 10⁹⁢(97-digit number)
12214630427767941043…02115010879531774719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.442 Γ— 10⁹⁢(97-digit number)
24429260855535882087…04230021759063549439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.885 Γ— 10⁹⁢(97-digit number)
48858521711071764174…08460043518127098879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.771 Γ— 10⁹⁢(97-digit number)
97717043422143528349…16920087036254197759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.954 Γ— 10⁹⁷(98-digit number)
19543408684428705669…33840174072508395519
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,599,247 XPMΒ·at block #6,794,401 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK