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Block #2,634,297

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 8:15:28 PM Β· Difficulty 11.2368 Β· 4,208,492 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
27f992a43bfab5feba328c58cbce8e4b4cfd4848fc1e73cf2ab0d83a7d0f25e6
View on Chainz β†—

Height

#2,634,297

Difficulty

11.236817

Transactions

2

Size

725 B

Version

2

Bits

0b3ca011

Nonce

298,624,369

Timestamp

4/28/2018, 8:15:28 PM

Confirmations

4,208,492

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

c32cafdf08c0f224d405907c2cb52d2fd7c0291e6af0e49a180134610e6a6d30
Transactions (2)
Coinbasee234fd8eab6fa7…a375f0cf1426ea
1 in β†’ 1 out7.9200 XPM110 B
Adqah8zh…1WwoHJ9t
5a0307844d7521…065f57d4ce574e
3 in β†’ 2 out363.3895 XPM524 B
ARTGxeAc…WmRAvHDaASbnn2Vs…1eCmu1FY
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.

1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368959
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
1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.917 Γ— 10⁹⁷(98-digit number)
19174421738023888881…14627799399267368961
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
3.834 Γ— 10⁹⁷(98-digit number)
38348843476047777763…29255598798534737919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.834 Γ— 10⁹⁷(98-digit number)
38348843476047777763…29255598798534737921
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
7.669 Γ— 10⁹⁷(98-digit number)
76697686952095555527…58511197597069475839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.669 Γ— 10⁹⁷(98-digit number)
76697686952095555527…58511197597069475841
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
1.533 Γ— 10⁹⁸(99-digit number)
15339537390419111105…17022395194138951679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.533 Γ— 10⁹⁸(99-digit number)
15339537390419111105…17022395194138951681
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
3.067 Γ— 10⁹⁸(99-digit number)
30679074780838222211…34044790388277903359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.067 Γ— 10⁹⁸(99-digit number)
30679074780838222211…34044790388277903361
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
6.135 Γ— 10⁹⁸(99-digit number)
61358149561676444422…68089580776555806719
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
6.135 Γ— 10⁹⁸(99-digit number)
61358149561676444422…68089580776555806721
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:57,986,650 XPMΒ·at block #6,842,788 Β· updates every 60s
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