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Block #2,732,669

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/3/2018, 3:22:23 PM Β· Difficulty 11.6319 Β· 4,106,066 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
93a3c46f6025b15c94c10b5b7fa9aac64c9eff2ec1ad003d720bb0e6e16c286c
View on Chainz β†—

Height

#2,732,669

Difficulty

11.631901

Transactions

3

Size

1.07 KB

Version

2

Bits

0ba1c446

Nonce

488,428,819

Timestamp

7/3/2018, 3:22:23 PM

Confirmations

4,106,066

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

afccebc94c2c5bcb129bf5717d26c8936955fedc57fd76d5f32ac68976a22455
Transactions (3)
Coinbaseda6a9849eaacf7…037e4ad1d7c723
1 in β†’ 1 out7.4000 XPM110 B
AZtxQr2F…7grUWrUz
d56edea4ddd7d2…9043fc6cb7341e
2 in β†’ 2 out5.1441 XPM375 B
AKBxhYmY…4XGb9PCfAPJQm6Pd…g3LTuiNL
10b8e3d92c91a8…703e37c856639f
3 in β†’ 2 out4.0471 XPM522 B
ALg819eB…kvTf2FuzAbU3e2GE…yGuY6jrW
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.

2.243 Γ— 10⁹⁡(96-digit number)
22435325961053562373…10596031307250449279
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
2.243 Γ— 10⁹⁡(96-digit number)
22435325961053562373…10596031307250449279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.487 Γ— 10⁹⁡(96-digit number)
44870651922107124746…21192062614500898559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.974 Γ— 10⁹⁡(96-digit number)
89741303844214249492…42384125229001797119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.794 Γ— 10⁹⁢(97-digit number)
17948260768842849898…84768250458003594239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.589 Γ— 10⁹⁢(97-digit number)
35896521537685699796…69536500916007188479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.179 Γ— 10⁹⁢(97-digit number)
71793043075371399593…39073001832014376959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.435 Γ— 10⁹⁷(98-digit number)
14358608615074279918…78146003664028753919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.871 Γ— 10⁹⁷(98-digit number)
28717217230148559837…56292007328057507839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.743 Γ— 10⁹⁷(98-digit number)
57434434460297119675…12584014656115015679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁸(99-digit number)
11486886892059423935…25168029312230031359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.297 Γ— 10⁹⁸(99-digit number)
22973773784118847870…50336058624460062719
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:57,954,137 XPMΒ·at block #6,838,734 Β· updates every 60s
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