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Block #2,160,508

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/14/2017, 3:41:12 PM Β· Difficulty 10.9014 Β· 4,670,038 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0d872be22a4faef6f7a725462ea408f4ff3d9b8e79616784d1620f161805fa90
View on Chainz β†—

Height

#2,160,508

Difficulty

10.901448

Transactions

1

Size

199 B

Version

2

Bits

0ae6c546

Nonce

545,714,609

Timestamp

6/14/2017, 3:41:12 PM

Confirmations

4,670,038

Mined by

⛏️ P2SHAY7ZqeDs1jRxNP9MX2rPpezc9eDu4z9aum

Merkle Root

0e3a77aaf3cc550188b513b423319999b9b3eafc17fc86b077dcbf60abc67f9a
Transactions (1)
Coinbase0e3a77aaf3cc55…dcbf60abc67f9a
1 in β†’ 1 out8.4000 XPM109 B
AY7ZqeDs…Du4z9aum
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.

4.356 Γ— 10⁹⁴(95-digit number)
43566870578213995962…41409815776165196799
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
4.356 Γ— 10⁹⁴(95-digit number)
43566870578213995962…41409815776165196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.713 Γ— 10⁹⁴(95-digit number)
87133741156427991924…82819631552330393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.742 Γ— 10⁹⁡(96-digit number)
17426748231285598384…65639263104660787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.485 Γ— 10⁹⁡(96-digit number)
34853496462571196769…31278526209321574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.970 Γ— 10⁹⁡(96-digit number)
69706992925142393539…62557052418643148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.394 Γ— 10⁹⁢(97-digit number)
13941398585028478707…25114104837286297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.788 Γ— 10⁹⁢(97-digit number)
27882797170056957415…50228209674572595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.576 Γ— 10⁹⁢(97-digit number)
55765594340113914831…00456419349145190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.115 Γ— 10⁹⁷(98-digit number)
11153118868022782966…00912838698290380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.230 Γ— 10⁹⁷(98-digit number)
22306237736045565932…01825677396580761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.461 Γ— 10⁹⁷(98-digit number)
44612475472091131865…03651354793161523199
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:57,888,617 XPMΒ·at block #6,830,545 Β· updates every 60s
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