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Block #647,268

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/25/2014, 11:40:04 AM Β· Difficulty 10.9518 Β· 6,155,405 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ff4761ae2b8808537f407c884329c1091fe3f2faa7159b39ceda3476b90ad7f4
View on Chainz β†—

Height

#647,268

Difficulty

10.951750

Transactions

2

Size

1.72 KB

Version

2

Bits

0af3a5e6

Nonce

152,346,848

Timestamp

7/25/2014, 11:40:04 AM

Confirmations

6,155,405

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

647eb0547b67fa8788e07c0c87a6a99e2f24fa98f8cbd6ffaab694f71f0a8af1
Transactions (2)
Coinbase207a3d7322f4ad…6ca8334632f13c
1 in β†’ 1 out8.3400 XPM116 B
ANSXnLY2…Sd25TjkD
64a1f5e9fe599f…a32616cc11eeb2
10 in β†’ 2 out10000.0100 XPM1.52 KB
Ae5WFHbn…gBo7rvHrAYktJ1ke…7cncjHv3
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.

3.054 Γ— 10⁹⁢(97-digit number)
30540883759158673242…30896068608922346879
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
3.054 Γ— 10⁹⁢(97-digit number)
30540883759158673242…30896068608922346879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.108 Γ— 10⁹⁢(97-digit number)
61081767518317346485…61792137217844693759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.221 Γ— 10⁹⁷(98-digit number)
12216353503663469297…23584274435689387519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.443 Γ— 10⁹⁷(98-digit number)
24432707007326938594…47168548871378775039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.886 Γ— 10⁹⁷(98-digit number)
48865414014653877188…94337097742757550079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.773 Γ— 10⁹⁷(98-digit number)
97730828029307754376…88674195485515100159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.954 Γ— 10⁹⁸(99-digit number)
19546165605861550875…77348390971030200319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.909 Γ— 10⁹⁸(99-digit number)
39092331211723101750…54696781942060400639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.818 Γ— 10⁹⁸(99-digit number)
78184662423446203501…09393563884120801279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.563 Γ— 10⁹⁹(100-digit number)
15636932484689240700…18787127768241602559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.127 Γ— 10⁹⁹(100-digit number)
31273864969378481400…37574255536483205119
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:57,665,404 XPMΒ·at block #6,802,672 Β· updates every 60s
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