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Block #2,133,539

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/26/2017, 2:27:21 PM Β· Difficulty 10.9094 Β· 4,709,582 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3e120f98881164fb8ce4c4eaf132114cae6fe9dfb3a852b0fc2ffe7e8627753a
View on Chainz β†—

Height

#2,133,539

Difficulty

10.909404

Transactions

1

Size

199 B

Version

2

Bits

0ae8ceb3

Nonce

1,269,819,535

Timestamp

5/26/2017, 2:27:21 PM

Confirmations

4,709,582

Mined by

⛏️ P2SHAXK959qtDiW37p353GF4sHMjcd16Duuqe3

Merkle Root

50ca52f1cca60e7591a710c769305874b15bcdcb5841c56512a0aab0746ded27
Transactions (1)
Coinbase50ca52f1cca60e…a0aab0746ded27
1 in β†’ 1 out8.3900 XPM109 B
AXK959qt…16Duuqe3
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.

5.243 Γ— 10⁹⁴(95-digit number)
52432765730452343901…10750485687393484799
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
5.243 Γ— 10⁹⁴(95-digit number)
52432765730452343901…10750485687393484799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.243 Γ— 10⁹⁴(95-digit number)
52432765730452343901…10750485687393484801
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
1.048 Γ— 10⁹⁡(96-digit number)
10486553146090468780…21500971374786969599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.048 Γ— 10⁹⁡(96-digit number)
10486553146090468780…21500971374786969601
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
2.097 Γ— 10⁹⁡(96-digit number)
20973106292180937560…43001942749573939199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.097 Γ— 10⁹⁡(96-digit number)
20973106292180937560…43001942749573939201
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
4.194 Γ— 10⁹⁡(96-digit number)
41946212584361875121…86003885499147878399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.194 Γ— 10⁹⁡(96-digit number)
41946212584361875121…86003885499147878401
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
8.389 Γ— 10⁹⁡(96-digit number)
83892425168723750242…72007770998295756799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.389 Γ— 10⁹⁡(96-digit number)
83892425168723750242…72007770998295756801
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
1.677 Γ— 10⁹⁢(97-digit number)
16778485033744750048…44015541996591513599
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:57,989,333 XPMΒ·at block #6,843,120 Β· updates every 60s
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