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Block #2,581,949

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/24/2018, 1:02:24 AM Β· Difficulty 11.1037 Β· 4,261,066 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2adceccd4fc96cea01931aa3c8917b7120f531a68c3972c2e4cf9e08a3d70827
View on Chainz β†—

Height

#2,581,949

Difficulty

11.103665

Transactions

2

Size

866 B

Version

2

Bits

0b1a89c6

Nonce

1,731,858,561

Timestamp

3/24/2018, 1:02:24 AM

Confirmations

4,261,066

Mined by

⛏️ P2SHAFvAq6HYgwDELswToCmwyx52EAspbRdr9a

Merkle Root

939019ad198bce57a594cd78be803adaa5155d4ffc811b01d70d4112d7f16f08
Transactions (2)
Coinbase03947e89263ecc…ae057fb1ef8c4d
1 in β†’ 1 out8.1100 XPM109 B
AFvAq6HY…spbRdr9a
fc658a575159b1…e426374c2ffa67
4 in β†’ 2 out16615.4741 XPM667 B
AT1bUu6o…owSzCB5oAGpNA4aA…6uPm59AD
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.

1.374 Γ— 10⁹⁡(96-digit number)
13744802298431325035…21529089205855027201
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.374 Γ— 10⁹⁡(96-digit number)
13744802298431325035…21529089205855027201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.748 Γ— 10⁹⁡(96-digit number)
27489604596862650070…43058178411710054401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.497 Γ— 10⁹⁡(96-digit number)
54979209193725300140…86116356823420108801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.099 Γ— 10⁹⁢(97-digit number)
10995841838745060028…72232713646840217601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.199 Γ— 10⁹⁢(97-digit number)
21991683677490120056…44465427293680435201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.398 Γ— 10⁹⁢(97-digit number)
43983367354980240112…88930854587360870401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.796 Γ— 10⁹⁢(97-digit number)
87966734709960480224…77861709174721740801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.759 Γ— 10⁹⁷(98-digit number)
17593346941992096044…55723418349443481601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.518 Γ— 10⁹⁷(98-digit number)
35186693883984192089…11446836698886963201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.037 Γ— 10⁹⁷(98-digit number)
70373387767968384179…22893673397773926401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.407 Γ— 10⁹⁸(99-digit number)
14074677553593676835…45787346795547852801
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,988,475 XPMΒ·at block #6,843,014 Β· updates every 60s
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