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Block #2,671,456

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/21/2018, 12:30:25 PM Β· Difficulty 11.6889 Β· 4,169,938 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2d8c00c252157d3e7a975d29877a33b5526224ebfa8a3e8c7c3cc2cea8105e0
View on Chainz β†—

Height

#2,671,456

Difficulty

11.688855

Transactions

2

Size

1017 B

Version

2

Bits

0bb058cb

Nonce

1,539,427,219

Timestamp

5/21/2018, 12:30:25 PM

Confirmations

4,169,938

Mined by

⛏️ P2SHAdhaq7ftHH8ExoFNeYgjNo8XL86NEGDvGB

Merkle Root

e24856748fdd6b767872d1922235abaf69f9b937826c1bb29b8c521c39560724
Transactions (2)
Coinbase06d2bb82e18408…da904c24564edb
1 in β†’ 1 out7.3200 XPM109 B
Adhaq7ft…6NEGDvGB
96ca766eb07ddc…20ce8cc70aef1a
5 in β†’ 2 out262.9693 XPM818 B
AMacMFhM…iFNVuut4AUn3a88N…5WM8WNLq
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.

1.300 Γ— 10⁹⁴(95-digit number)
13000954427799129919…00472453826707148221
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
1.300 Γ— 10⁹⁴(95-digit number)
13000954427799129919…00472453826707148221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.600 Γ— 10⁹⁴(95-digit number)
26001908855598259838…00944907653414296441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.200 Γ— 10⁹⁴(95-digit number)
52003817711196519676…01889815306828592881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.040 Γ— 10⁹⁡(96-digit number)
10400763542239303935…03779630613657185761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.080 Γ— 10⁹⁡(96-digit number)
20801527084478607870…07559261227314371521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.160 Γ— 10⁹⁡(96-digit number)
41603054168957215741…15118522454628743041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
8.320 Γ— 10⁹⁡(96-digit number)
83206108337914431482…30237044909257486081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.664 Γ— 10⁹⁢(97-digit number)
16641221667582886296…60474089818514972161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.328 Γ— 10⁹⁢(97-digit number)
33282443335165772592…20948179637029944321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
6.656 Γ— 10⁹⁢(97-digit number)
66564886670331545185…41896359274059888641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.331 Γ— 10⁹⁷(98-digit number)
13312977334066309037…83792718548119777281
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:57,975,524 XPMΒ·at block #6,841,393 Β· updates every 60s
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