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Block #103,991

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2013, 8:24:12 PM Β· Difficulty 9.5440 Β· 6,722,969 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a7e9fe908be4110a83dd4e54dffb48f1a3b51546c52e0de404d62588852c8c05
View on Chainz β†—

Height

#103,991

Difficulty

9.543983

Transactions

2

Size

1.16 KB

Version

2

Bits

098b427f

Nonce

96,826

Timestamp

8/7/2013, 8:24:12 PM

Confirmations

6,722,969

Mined by

⛏️ P2SHAG7ottr6Qs8chV54HYV6MWq39U9HFPssth

Merkle Root

a02a28199758116ec7b5dcb7438a9183a8e11c01f49b5458770c55617876135b
Transactions (2)
Coinbasea4c66bdcb4a79d…06687ded32d852
1 in β†’ 1 out10.9700 XPM109 B
AG7ottr6…9HFPssth
c575dbcd67f461…843b859b10b40f
8 in β†’ 2 out90.1200 XPM992 B
AcMTzmRW…9i3snmhLAX7HepGv…Qm28ooHF
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.

2.860 Γ— 10⁹⁢(97-digit number)
28602612916398480285…49931739339961955119
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
2.860 Γ— 10⁹⁢(97-digit number)
28602612916398480285…49931739339961955119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.720 Γ— 10⁹⁢(97-digit number)
57205225832796960571…99863478679923910239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.144 Γ— 10⁹⁷(98-digit number)
11441045166559392114…99726957359847820479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.288 Γ— 10⁹⁷(98-digit number)
22882090333118784228…99453914719695640959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.576 Γ— 10⁹⁷(98-digit number)
45764180666237568456…98907829439391281919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.152 Γ— 10⁹⁷(98-digit number)
91528361332475136913…97815658878782563839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.830 Γ— 10⁹⁸(99-digit number)
18305672266495027382…95631317757565127679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.661 Γ— 10⁹⁸(99-digit number)
36611344532990054765…91262635515130255359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.322 Γ— 10⁹⁸(99-digit number)
73222689065980109531…82525271030260510719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,859,856 XPMΒ·at block #6,826,959 Β· updates every 60s
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