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Block #668,346

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2014, 4:52:40 AM Β· Difficulty 10.9635 Β· 6,138,643 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
87a6c065dd80f9a6b29793aa3ec5c6840e2a2f4b477d518fb2af48275837ca26
View on Chainz β†—

Height

#668,346

Difficulty

10.963464

Transactions

2

Size

431 B

Version

2

Bits

0af6a594

Nonce

2,613,796,018

Timestamp

8/8/2014, 4:52:40 AM

Confirmations

6,138,643

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c0c2e06673c137fcb7ac3483b15ef4286c233c834dfa463b49882edab0c5353a
Transactions (2)
Coinbase1e07164196c96a…52295f8140d960
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
02daf7e4639015…115424dce07ca8
1 in β†’ 2 out5.5986 XPM225 B
ASEkR768…35s3LmSuARvFZvCQ…VopF1xmb
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.

1.375 Γ— 10⁹⁡(96-digit number)
13758297589471720770…51504757807160097759
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
1.375 Γ— 10⁹⁡(96-digit number)
13758297589471720770…51504757807160097759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.751 Γ— 10⁹⁡(96-digit number)
27516595178943441541…03009515614320195519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.503 Γ— 10⁹⁡(96-digit number)
55033190357886883082…06019031228640391039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁢(97-digit number)
11006638071577376616…12038062457280782079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.201 Γ— 10⁹⁢(97-digit number)
22013276143154753233…24076124914561564159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.402 Γ— 10⁹⁢(97-digit number)
44026552286309506466…48152249829123128319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.805 Γ— 10⁹⁢(97-digit number)
88053104572619012932…96304499658246256639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁷(98-digit number)
17610620914523802586…92608999316492513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.522 Γ— 10⁹⁷(98-digit number)
35221241829047605173…85217998632985026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.044 Γ— 10⁹⁷(98-digit number)
70442483658095210346…70435997265970053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.408 Γ— 10⁹⁸(99-digit number)
14088496731619042069…40871994531940106239
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:57,700,015 XPMΒ·at block #6,806,988 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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