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Block #707,692

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/5/2014, 3:06:27 AM Β· Difficulty 10.9580 Β· 6,094,815 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4aae42a373cff28ece997e7e4999a3aab3b7a65c44443abc766929b58409e301
View on Chainz β†—

Height

#707,692

Difficulty

10.957955

Transactions

2

Size

399 B

Version

2

Bits

0af53c85

Nonce

564,618,530

Timestamp

9/5/2014, 3:06:27 AM

Confirmations

6,094,815

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b3163479fd5105665cacc186aafd69d163b0b0f15050cd5f3a24b4f303ad9d5b
Transactions (2)
Coinbase724a255caa2f39…99db2273b0be14
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
b243235296f4f8…52305a751c3d67
1 in β†’ 2 out8.3000 XPM193 B
AUHFmvnF…juaRoiLdAeKNrjNj…1NEq95Ta
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.

6.864 Γ— 10⁹⁴(95-digit number)
68649577990285188963…49608958650698843839
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
6.864 Γ— 10⁹⁴(95-digit number)
68649577990285188963…49608958650698843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.372 Γ— 10⁹⁡(96-digit number)
13729915598057037792…99217917301397687679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.745 Γ— 10⁹⁡(96-digit number)
27459831196114075585…98435834602795375359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.491 Γ— 10⁹⁡(96-digit number)
54919662392228151171…96871669205590750719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.098 Γ— 10⁹⁢(97-digit number)
10983932478445630234…93743338411181501439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.196 Γ— 10⁹⁢(97-digit number)
21967864956891260468…87486676822363002879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.393 Γ— 10⁹⁢(97-digit number)
43935729913782520936…74973353644726005759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.787 Γ— 10⁹⁢(97-digit number)
87871459827565041873…49946707289452011519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.757 Γ— 10⁹⁷(98-digit number)
17574291965513008374…99893414578904023039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.514 Γ— 10⁹⁷(98-digit number)
35148583931026016749…99786829157808046079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.029 Γ— 10⁹⁷(98-digit number)
70297167862052033498…99573658315616092159
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:57,664,063 XPMΒ·at block #6,802,506 Β· updates every 60s
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