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Block #2,169,978

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/21/2017, 6:07:51 AM Β· Difficulty 10.9010 Β· 4,666,698 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2ac6c7f5d899885c39fb4183bec0d7daf09483c496a39a60c31ebab90632f86c
View on Chainz β†—

Height

#2,169,978

Difficulty

10.901029

Transactions

1

Size

199 B

Version

2

Bits

0ae6a9dc

Nonce

28,416,955

Timestamp

6/21/2017, 6:07:51 AM

Confirmations

4,666,698

Mined by

⛏️ P2SHAVhkPVUgqqzfRR4rhsuZ3JH2boNFYMaYsz

Merkle Root

b00d17b8d6a0df61e5026b2e1287cd760a4f79d8e14e0dcfd289cff21c274cf2
Transactions (1)
Coinbaseb00d17b8d6a0df…89cff21c274cf2
1 in β†’ 1 out8.4000 XPM109 B
AVhkPVUg…NFYMaYsz
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.

8.934 Γ— 10⁹³(94-digit number)
89343667072119523018…04591311680789666859
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
8.934 Γ— 10⁹³(94-digit number)
89343667072119523018…04591311680789666859
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁴(95-digit number)
17868733414423904603…09182623361579333719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁴(95-digit number)
35737466828847809207…18365246723158667439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.147 Γ— 10⁹⁴(95-digit number)
71474933657695618414…36730493446317334879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.429 Γ— 10⁹⁡(96-digit number)
14294986731539123682…73460986892634669759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.858 Γ— 10⁹⁡(96-digit number)
28589973463078247365…46921973785269339519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.717 Γ— 10⁹⁡(96-digit number)
57179946926156494731…93843947570538679039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.143 Γ— 10⁹⁢(97-digit number)
11435989385231298946…87687895141077358079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.287 Γ— 10⁹⁢(97-digit number)
22871978770462597892…75375790282154716159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.574 Γ— 10⁹⁢(97-digit number)
45743957540925195785…50751580564309432319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.148 Γ— 10⁹⁢(97-digit number)
91487915081850391570…01503161128618864639
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:57,937,688 XPMΒ·at block #6,836,675 Β· updates every 60s
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