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Block #2,814,849

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/29/2018, 5:20:59 AM Β· Difficulty 11.6825 Β· 4,011,383 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
6f517af1c8a6e41b3b36d8c38fdfb1c8149f4deb01beaff2f25df98439aced4f
View on Chainz β†—

Height

#2,814,849

Difficulty

11.682479

Transactions

2

Size

37.55 KB

Version

2

Bits

0baeb6f0

Nonce

1,704,041,232

Timestamp

8/29/2018, 5:20:59 AM

Confirmations

4,011,383

Mined by

⛏️ P2SHAUCtxbgVtW3dKefLYiTzAkZwTNVNcSSGQm

Merkle Root

69e0acf4a4cbcf67065f007f259681d0b00b625a2015983ba1820921c6d02708
Transactions (2)
Coinbase87886a1b1a6cc8…166e4484e52dd1
1 in β†’ 1 out7.7000 XPM110 B
AUCtxbgV…VNcSSGQm
ac12cbea429043…6bd9c751d97cec
258 in β†’ 2 out2203.9571 XPM37.36 KB
AVa5dYbR…j5uZYCvtAKYPff8D…LABEHnS9
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.

2.036 Γ— 10⁹⁴(95-digit number)
20366015719191559912…17535574864183976159
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.036 Γ— 10⁹⁴(95-digit number)
20366015719191559912…17535574864183976159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.036 Γ— 10⁹⁴(95-digit number)
20366015719191559912…17535574864183976161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.073 Γ— 10⁹⁴(95-digit number)
40732031438383119824…35071149728367952319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.073 Γ— 10⁹⁴(95-digit number)
40732031438383119824…35071149728367952321
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
8.146 Γ— 10⁹⁴(95-digit number)
81464062876766239648…70142299456735904639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.146 Γ— 10⁹⁴(95-digit number)
81464062876766239648…70142299456735904641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.629 Γ— 10⁹⁡(96-digit number)
16292812575353247929…40284598913471809279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.629 Γ— 10⁹⁡(96-digit number)
16292812575353247929…40284598913471809281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.258 Γ— 10⁹⁡(96-digit number)
32585625150706495859…80569197826943618559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.258 Γ— 10⁹⁡(96-digit number)
32585625150706495859…80569197826943618561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
6.517 Γ— 10⁹⁡(96-digit number)
65171250301412991718…61138395653887237119
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 Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,853,987 XPMΒ·at block #6,826,231 Β· updates every 60s
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