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Block #2,660,077

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/14/2018, 3:21:51 AM Β· Difficulty 11.6385 Β· 4,182,072 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3b8572d565299e6d547b7f74dbebc31524c893561d2d2927e243ad28811f3bc3
View on Chainz β†—

Height

#2,660,077

Difficulty

11.638458

Transactions

2

Size

1.28 KB

Version

2

Bits

0ba37201

Nonce

241,471,463

Timestamp

5/14/2018, 3:21:51 AM

Confirmations

4,182,072

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

ffdee1d1feed891c0ebc3d1c6cea0840935e75e3bb4c42444109f4d97698d89d
Transactions (2)
Coinbase69ad82dda65359…7f6d44076d8c06
1 in β†’ 1 out7.3900 XPM110 B
Adqah8zh…1WwoHJ9t
95ddd8784d54e1…7cbe6d841738be
7 in β†’ 2 out31.1388 XPM1.09 KB
AdepddBi…eU9B97ytAcCev8MG…dc3yRPG3
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.

7.372 Γ— 10⁹⁴(95-digit number)
73727256863775164432…16862263372436414239
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
7.372 Γ— 10⁹⁴(95-digit number)
73727256863775164432…16862263372436414239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.372 Γ— 10⁹⁴(95-digit number)
73727256863775164432…16862263372436414241
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
1.474 Γ— 10⁹⁡(96-digit number)
14745451372755032886…33724526744872828479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.474 Γ— 10⁹⁡(96-digit number)
14745451372755032886…33724526744872828481
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
2.949 Γ— 10⁹⁡(96-digit number)
29490902745510065773…67449053489745656959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.949 Γ— 10⁹⁡(96-digit number)
29490902745510065773…67449053489745656961
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
5.898 Γ— 10⁹⁡(96-digit number)
58981805491020131546…34898106979491313919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.898 Γ— 10⁹⁡(96-digit number)
58981805491020131546…34898106979491313921
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
1.179 Γ— 10⁹⁢(97-digit number)
11796361098204026309…69796213958982627839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.179 Γ— 10⁹⁢(97-digit number)
11796361098204026309…69796213958982627841
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
2.359 Γ— 10⁹⁢(97-digit number)
23592722196408052618…39592427917965255679
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
2.359 Γ— 10⁹⁢(97-digit number)
23592722196408052618…39592427917965255681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 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
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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:57,981,581 XPMΒ·at block #6,842,148 Β· updates every 60s
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