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Block #969,603

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/11/2015, 4:55:37 PM Β· Difficulty 10.8321 Β· 5,872,180 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
59c04756e5a21ed1a1850c4be5766fa551d8153addf77e555f3194ca83db64e6
View on Chainz β†—

Height

#969,603

Difficulty

10.832119

Transactions

2

Size

1.58 KB

Version

2

Bits

0ad505ba

Nonce

819,602,166

Timestamp

3/11/2015, 4:55:37 PM

Confirmations

5,872,180

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c938239efcc653ccdf0a2688225fa40b7b8f60e7f1f24365cffff1a325c571ad
Transactions (2)
Coinbase754a49445edf6b…5eaedfe780e263
1 in β†’ 1 out8.5300 XPM116 B
ANSXnLY2…Sd25TjkD
c14881b77c2c7b…4c4ea5439db154
9 in β†’ 2 out32.4129 XPM1.38 KB
AM3BBVDL…f3ADKyXMAdi9Hvxm…agJsy1Lf
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.

5.229 Γ— 10⁹⁴(95-digit number)
52298482830227113537…39406775363835078759
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
5.229 Γ— 10⁹⁴(95-digit number)
52298482830227113537…39406775363835078759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.045 Γ— 10⁹⁡(96-digit number)
10459696566045422707…78813550727670157519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.091 Γ— 10⁹⁡(96-digit number)
20919393132090845414…57627101455340315039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.183 Γ— 10⁹⁡(96-digit number)
41838786264181690829…15254202910680630079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.367 Γ— 10⁹⁡(96-digit number)
83677572528363381659…30508405821361260159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.673 Γ— 10⁹⁢(97-digit number)
16735514505672676331…61016811642722520319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.347 Γ— 10⁹⁢(97-digit number)
33471029011345352663…22033623285445040639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.694 Γ— 10⁹⁢(97-digit number)
66942058022690705327…44067246570890081279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.338 Γ— 10⁹⁷(98-digit number)
13388411604538141065…88134493141780162559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.677 Γ— 10⁹⁷(98-digit number)
26776823209076282131…76268986283560325119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
5.355 Γ— 10⁹⁷(98-digit number)
53553646418152564262…52537972567120650239
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:57,978,641 XPMΒ·at block #6,841,782 Β· updates every 60s
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