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Block #2,676,546

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/24/2018, 10:59:42 PM Β· Difficulty 11.6976 Β· 4,165,809 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ae4e549ed47e8d9f42729ee5cabe612bcff72aa13520919a46f1162e3cfd9aac
View on Chainz β†—

Height

#2,676,546

Difficulty

11.697613

Transactions

1

Size

201 B

Version

2

Bits

0bb296c2

Nonce

291,952,189

Timestamp

5/24/2018, 10:59:42 PM

Confirmations

4,165,809

Mined by

⛏️ P2SHALNDWtiE4USrwBmskKgdpuA5mqzgBCZFuC

Merkle Root

7a610a6f2b42738d2964e53b8f0c1d4cd7b9bd1b8216786f70e6cfda7d9b84e3
Transactions (1)
Coinbase7a610a6f2b4273…e6cfda7d9b84e3
1 in β†’ 1 out7.3000 XPM110 B
ALNDWtiE…zgBCZFuC
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.

9.353 Γ— 10⁹⁡(96-digit number)
93531887359579821318…09219389161389347839
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
9.353 Γ— 10⁹⁡(96-digit number)
93531887359579821318…09219389161389347839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.353 Γ— 10⁹⁡(96-digit number)
93531887359579821318…09219389161389347841
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
1.870 Γ— 10⁹⁢(97-digit number)
18706377471915964263…18438778322778695679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.870 Γ— 10⁹⁢(97-digit number)
18706377471915964263…18438778322778695681
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
3.741 Γ— 10⁹⁢(97-digit number)
37412754943831928527…36877556645557391359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.741 Γ— 10⁹⁢(97-digit number)
37412754943831928527…36877556645557391361
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
7.482 Γ— 10⁹⁢(97-digit number)
74825509887663857054…73755113291114782719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.482 Γ— 10⁹⁢(97-digit number)
74825509887663857054…73755113291114782721
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
1.496 Γ— 10⁹⁷(98-digit number)
14965101977532771410…47510226582229565439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.496 Γ— 10⁹⁷(98-digit number)
14965101977532771410…47510226582229565441
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
2.993 Γ— 10⁹⁷(98-digit number)
29930203955065542821…95020453164459130879
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:57,983,247 XPMΒ·at block #6,842,354 Β· updates every 60s
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