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Block #1,542,493

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/15/2016, 1:14:53 PM Β· Difficulty 10.6481 Β· 5,284,581 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d33476dc66a87064600bd9b9dad0b8a1d201fc59115647009c5061b07523247b
View on Chainz β†—

Height

#1,542,493

Difficulty

10.648078

Transactions

2

Size

2.44 KB

Version

2

Bits

0aa5e871

Nonce

435,568,869

Timestamp

4/15/2016, 1:14:53 PM

Confirmations

5,284,581

Mined by

⛏️ P2SHAStYBBF5XGW4BwU4ZeC96pCQfWmspP9Fkf

Merkle Root

1dcfcba20994cb81069f032bdd2af379e91fcaa0f15d11bd5dbe16612a136162
Transactions (2)
Coinbasede9f570b878539…85615afb6db93b
1 in β†’ 1 out8.8400 XPM109 B
AStYBBF5…mspP9Fkf
275ef7c26a5ed9…816adf78bb2510
15 in β†’ 2 out0.3707 XPM2.25 KB
AWXUrMFe…WPEz5FykAcSSz2aF…pA3smH8j
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.

5.669 Γ— 10⁹⁷(98-digit number)
56699433705438730601…37346695491281879039
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
5.669 Γ— 10⁹⁷(98-digit number)
56699433705438730601…37346695491281879039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.669 Γ— 10⁹⁷(98-digit number)
56699433705438730601…37346695491281879041
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
1.133 Γ— 10⁹⁸(99-digit number)
11339886741087746120…74693390982563758079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.133 Γ— 10⁹⁸(99-digit number)
11339886741087746120…74693390982563758081
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
2.267 Γ— 10⁹⁸(99-digit number)
22679773482175492240…49386781965127516159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.267 Γ— 10⁹⁸(99-digit number)
22679773482175492240…49386781965127516161
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
4.535 Γ— 10⁹⁸(99-digit number)
45359546964350984481…98773563930255032319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.535 Γ— 10⁹⁸(99-digit number)
45359546964350984481…98773563930255032321
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
9.071 Γ— 10⁹⁸(99-digit number)
90719093928701968962…97547127860510064639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.071 Γ— 10⁹⁸(99-digit number)
90719093928701968962…97547127860510064641
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,860,775 XPMΒ·at block #6,827,073 Β· updates every 60s
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