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Block #1,534,799

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/10/2016, 11:46:49 AM Β· Difficulty 10.6182 Β· 5,279,255 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
c5f39bac246e0d7a01c2bbffa9fdaf12a9d94490f9334e35f850b9a6c9747d87
View on Chainz β†—

Height

#1,534,799

Difficulty

10.618234

Transactions

2

Size

7.61 KB

Version

2

Bits

0a9e449c

Nonce

1,761,161,030

Timestamp

4/10/2016, 11:46:49 AM

Confirmations

5,279,255

Mined by

⛏️ P2SHAJVhv9KtesQN3r2PoAj85MjC1awWXcYvhK

Merkle Root

fe526b0a8bc8da9488c515b7f44d8601a63808a2d0e2a244987ca89f9a47404f
Transactions (2)
Coinbase67403d649b646a…d109689521fb9c
1 in β†’ 1 out8.9400 XPM109 B
AJVhv9Kt…wWXcYvhK
dc29861f0cd2f3…3e8b6f27419d83
51 in β†’ 1 out1505.3436 XPM7.42 KB
AV6PxrSB…gKr8Hu3V
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.

2.804 Γ— 10⁹⁷(98-digit number)
28046113264198579239…49564192154279690239
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
2.804 Γ— 10⁹⁷(98-digit number)
28046113264198579239…49564192154279690239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.804 Γ— 10⁹⁷(98-digit number)
28046113264198579239…49564192154279690241
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
5.609 Γ— 10⁹⁷(98-digit number)
56092226528397158479…99128384308559380479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.609 Γ— 10⁹⁷(98-digit number)
56092226528397158479…99128384308559380481
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
1.121 Γ— 10⁹⁸(99-digit number)
11218445305679431695…98256768617118760959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.121 Γ— 10⁹⁸(99-digit number)
11218445305679431695…98256768617118760961
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
2.243 Γ— 10⁹⁸(99-digit number)
22436890611358863391…96513537234237521919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.243 Γ— 10⁹⁸(99-digit number)
22436890611358863391…96513537234237521921
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
4.487 Γ— 10⁹⁸(99-digit number)
44873781222717726783…93027074468475043839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.487 Γ— 10⁹⁸(99-digit number)
44873781222717726783…93027074468475043841
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:57,756,508 XPMΒ·at block #6,814,053 Β· updates every 60s
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