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Block #2,756,537

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2018, 9:17:44 PM Β· Difficulty 11.6656 Β· 4,080,184 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2111afde786ba666a5c6e5e09fac477a3ac408dfffe2e2feb79f2f8be299ecce
View on Chainz β†—

Height

#2,756,537

Difficulty

11.665557

Transactions

1

Size

200 B

Version

2

Bits

0baa61f0

Nonce

500,845,305

Timestamp

7/19/2018, 9:17:44 PM

Confirmations

4,080,184

Mined by

⛏️ P2SHAQuYtLfgEhrPcWJ7McTycHCEuadGfJJxaW

Merkle Root

5726112e8c04f948f8c8bf965ddde9a55836c709d9e8af4494385a132097b0b2
Transactions (1)
Coinbase5726112e8c04f9…385a132097b0b2
1 in β†’ 1 out7.3400 XPM110 B
AQuYtLfg…dGfJJxaW
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.

1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149599
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
1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149601
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
2.318 Γ— 10⁹⁡(96-digit number)
23184050335638407998…28147949317740299199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.318 Γ— 10⁹⁡(96-digit number)
23184050335638407998…28147949317740299201
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
4.636 Γ— 10⁹⁡(96-digit number)
46368100671276815997…56295898635480598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.636 Γ— 10⁹⁡(96-digit number)
46368100671276815997…56295898635480598401
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
9.273 Γ— 10⁹⁡(96-digit number)
92736201342553631994…12591797270961196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.273 Γ— 10⁹⁡(96-digit number)
92736201342553631994…12591797270961196801
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
1.854 Γ— 10⁹⁢(97-digit number)
18547240268510726398…25183594541922393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.854 Γ— 10⁹⁢(97-digit number)
18547240268510726398…25183594541922393601
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
3.709 Γ— 10⁹⁢(97-digit number)
37094480537021452797…50367189083844787199
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:57,938,050 XPMΒ·at block #6,836,720 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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