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Block #2,753,726

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2018, 1:05:14 AM Β· Difficulty 11.6548 Β· 4,079,655 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
266b5d7250e33d6873e382e648213317aa34a5a3ee6d6c7a928909771a6602ea
View on Chainz β†—

Height

#2,753,726

Difficulty

11.654819

Transactions

2

Size

870 B

Version

2

Bits

0ba7a236

Nonce

147,073,807

Timestamp

7/18/2018, 1:05:14 AM

Confirmations

4,079,655

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

1796b98431b06a2e16172dfb137791d178675cb2259b42f212ee5d8f4444c400
Transactions (2)
Coinbase688854ce7e5152…daa30d32cb8989
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
55ac1a8f704409…0ea742b8d8d625
4 in β†’ 2 out3138.0308 XPM670 B
ATLw4wqX…kGTEjXFmAWE9yMjM…8D9i1Z1t
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.

2.732 Γ— 10⁹⁴(95-digit number)
27326123049877415934…10886789028076215759
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
2.732 Γ— 10⁹⁴(95-digit number)
27326123049877415934…10886789028076215759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.732 Γ— 10⁹⁴(95-digit number)
27326123049877415934…10886789028076215761
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
5.465 Γ— 10⁹⁴(95-digit number)
54652246099754831868…21773578056152431519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.465 Γ— 10⁹⁴(95-digit number)
54652246099754831868…21773578056152431521
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
1.093 Γ— 10⁹⁡(96-digit number)
10930449219950966373…43547156112304863039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.093 Γ— 10⁹⁡(96-digit number)
10930449219950966373…43547156112304863041
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
2.186 Γ— 10⁹⁡(96-digit number)
21860898439901932747…87094312224609726079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.186 Γ— 10⁹⁡(96-digit number)
21860898439901932747…87094312224609726081
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
4.372 Γ— 10⁹⁡(96-digit number)
43721796879803865494…74188624449219452159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.372 Γ— 10⁹⁡(96-digit number)
43721796879803865494…74188624449219452161
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
8.744 Γ— 10⁹⁡(96-digit number)
87443593759607730989…48377248898438904319
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
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