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Block #2,813,632

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/28/2018, 9:58:09 AM Β· Difficulty 11.6789 Β· 4,030,895 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a5ad177e575bf24e8bc467b284fbc9f013eb7dbf5a72f1858d9fda8e0037f04c
View on Chainz β†—

Height

#2,813,632

Difficulty

11.678873

Transactions

1

Size

200 B

Version

2

Bits

0badca9a

Nonce

18,265,573

Timestamp

8/28/2018, 9:58:09 AM

Confirmations

4,030,895

Mined by

⛏️ P2SHAHdt8GEMcKPyewYjomjiAnydxjrGMjdfiU

Merkle Root

dfadf4d2923b92b22559abe1c8bd42c56bf1f5170cb5f34b4f51527dca1279d8
Transactions (1)
Coinbasedfadf4d2923b92…51527dca1279d8
1 in β†’ 1 out7.3200 XPM110 B
AHdt8GEM…rGMjdfiU
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.

5.786 Γ— 10⁹⁴(95-digit number)
57868312523688923963…80411475356476640959
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
5.786 Γ— 10⁹⁴(95-digit number)
57868312523688923963…80411475356476640959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.786 Γ— 10⁹⁴(95-digit number)
57868312523688923963…80411475356476640961
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
1.157 Γ— 10⁹⁡(96-digit number)
11573662504737784792…60822950712953281919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.157 Γ— 10⁹⁡(96-digit number)
11573662504737784792…60822950712953281921
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
2.314 Γ— 10⁹⁡(96-digit number)
23147325009475569585…21645901425906563839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.314 Γ— 10⁹⁡(96-digit number)
23147325009475569585…21645901425906563841
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
4.629 Γ— 10⁹⁡(96-digit number)
46294650018951139170…43291802851813127679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.629 Γ— 10⁹⁡(96-digit number)
46294650018951139170…43291802851813127681
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
9.258 Γ— 10⁹⁡(96-digit number)
92589300037902278341…86583605703626255359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.258 Γ— 10⁹⁡(96-digit number)
92589300037902278341…86583605703626255361
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
1.851 Γ— 10⁹⁢(97-digit number)
18517860007580455668…73167211407252510719
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:58,000,616 XPMΒ·at block #6,844,526 Β· updates every 60s
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