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Block #2,757,003

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/20/2018, 5:16:29 AM Β· Difficulty 11.6648 Β· 4,076,738 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a0dc0ac47e5399331a06d8c32f557625d559be882da3b8a50add9908eb52c7d
View on Chainz β†—

Height

#2,757,003

Difficulty

11.664847

Transactions

2

Size

30.73 KB

Version

2

Bits

0baa336a

Nonce

212,961,375

Timestamp

7/20/2018, 5:16:29 AM

Confirmations

4,076,738

Mined by

⛏️ P2SHAKUGPAM8ToW9rSLhBQ1iRPHCA4jRVH8Yfv

Merkle Root

cd7fe8545df893099666b20c94147c9ef48bb35c5cff806b40918eaebad6d132
Transactions (2)
Coinbase0b02d00a486173…77db2b9a3bdd6c
1 in β†’ 1 out7.6600 XPM110 B
AKUGPAM8…jRVH8Yfv
50da7b65ffecf0…a35058c3f207c8
211 in β†’ 1 out11728.1805 XPM30.54 KB
ALPF8J52…Hjw4BMsG
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.

1.117 Γ— 10⁹⁸(99-digit number)
11177709818091168627…58568227379090124799
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
1.117 Γ— 10⁹⁸(99-digit number)
11177709818091168627…58568227379090124799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.117 Γ— 10⁹⁸(99-digit number)
11177709818091168627…58568227379090124801
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
2.235 Γ— 10⁹⁸(99-digit number)
22355419636182337254…17136454758180249599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.235 Γ— 10⁹⁸(99-digit number)
22355419636182337254…17136454758180249601
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
4.471 Γ— 10⁹⁸(99-digit number)
44710839272364674508…34272909516360499199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.471 Γ— 10⁹⁸(99-digit number)
44710839272364674508…34272909516360499201
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
8.942 Γ— 10⁹⁸(99-digit number)
89421678544729349017…68545819032720998399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.942 Γ— 10⁹⁸(99-digit number)
89421678544729349017…68545819032720998401
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
1.788 Γ— 10⁹⁹(100-digit number)
17884335708945869803…37091638065441996799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.788 Γ— 10⁹⁹(100-digit number)
17884335708945869803…37091638065441996801
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
3.576 Γ— 10⁹⁹(100-digit number)
35768671417891739606…74183276130883993599
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:57,914,146 XPMΒ·at block #6,833,740 Β· updates every 60s
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