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Block #3,146,522

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/19/2019, 5:31:33 PM Β· Difficulty 11.3230 Β· 3,694,049 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1202776fd67cceaf5d5163fe01d5c0b1b3eba3588477846dc79c25e661a2c4e4
View on Chainz β†—

Height

#3,146,522

Difficulty

11.322989

Transactions

2

Size

572 B

Version

2

Bits

0b52af6c

Nonce

81,265,093

Timestamp

4/19/2019, 5:31:33 PM

Confirmations

3,694,049

Mined by

⛏️ P2SHALQGpaT6bUeDR1X73XRmMe4Z6w9dLVU1B9

Merkle Root

d639bf7d7c4c8a34a9f926b52883d5983bf84b0decdc30b0ce0e2687c6bb8ed1
Transactions (2)
Coinbase0783361e1722ee…406c8b0d5389e2
1 in β†’ 1 out7.8000 XPM109 B
ALQGpaT6…9dLVU1B9
b1db4676f187b3…0e3aa6ec801d57
2 in β†’ 2 out1418.1069 XPM373 B
ASd4WGDY…TjGWRWbAAeTHTL7A…vT1872bk
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.

1.889 Γ— 10⁹⁡(96-digit number)
18896787921876725121…16507497170999030399
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
1.889 Γ— 10⁹⁡(96-digit number)
18896787921876725121…16507497170999030399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.779 Γ— 10⁹⁡(96-digit number)
37793575843753450243…33014994341998060799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.558 Γ— 10⁹⁡(96-digit number)
75587151687506900487…66029988683996121599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.511 Γ— 10⁹⁢(97-digit number)
15117430337501380097…32059977367992243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.023 Γ— 10⁹⁢(97-digit number)
30234860675002760195…64119954735984486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.046 Γ— 10⁹⁢(97-digit number)
60469721350005520390…28239909471968972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.209 Γ— 10⁹⁷(98-digit number)
12093944270001104078…56479818943937945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.418 Γ— 10⁹⁷(98-digit number)
24187888540002208156…12959637887875891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.837 Γ— 10⁹⁷(98-digit number)
48375777080004416312…25919275775751782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.675 Γ— 10⁹⁷(98-digit number)
96751554160008832624…51838551551503564799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.935 Γ— 10⁹⁸(99-digit number)
19350310832001766524…03677103103007129599
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:57,968,903 XPMΒ·at block #6,840,570 Β· updates every 60s
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