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Block #1,643,599

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/24/2016, 1:42:58 PM Β· Difficulty 10.6711 Β· 5,170,528 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
bbda7ccd943d18567db8640fa8ef3983bb6d2e9cf36d02d7dc7197e4bf0dae38
View on Chainz β†—

Height

#1,643,599

Difficulty

10.671090

Transactions

2

Size

2.98 KB

Version

2

Bits

0aabcc95

Nonce

246,969,589

Timestamp

6/24/2016, 1:42:58 PM

Confirmations

5,170,528

Mined by

⛏️ P2SHAKhGchUWjLsfwzixobs9671erPXEmMvYyi

Merkle Root

bc11ff172e29be3d8f67e40c233ac61c1dadf5c8d4224698af15c2fcb82013b3
Transactions (2)
Coinbase58f7c17be5e4c5…f5e96d6a7d97b8
1 in β†’ 1 out8.8100 XPM110 B
AKhGchUW…XEmMvYyi
e3afdf8a41e5c3…3969e250e0afd9
19 in β†’ 1 out1999.9900 XPM2.78 KB
AeGZ1Apc…Z6dDy7qA
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.

2.533 Γ— 10⁹⁡(96-digit number)
25332583085431502794…45800047446162817599
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
2.533 Γ— 10⁹⁡(96-digit number)
25332583085431502794…45800047446162817599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.533 Γ— 10⁹⁡(96-digit number)
25332583085431502794…45800047446162817601
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
5.066 Γ— 10⁹⁡(96-digit number)
50665166170863005588…91600094892325635199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.066 Γ— 10⁹⁡(96-digit number)
50665166170863005588…91600094892325635201
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
1.013 Γ— 10⁹⁢(97-digit number)
10133033234172601117…83200189784651270399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.013 Γ— 10⁹⁢(97-digit number)
10133033234172601117…83200189784651270401
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
2.026 Γ— 10⁹⁢(97-digit number)
20266066468345202235…66400379569302540799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.026 Γ— 10⁹⁢(97-digit number)
20266066468345202235…66400379569302540801
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
4.053 Γ— 10⁹⁢(97-digit number)
40532132936690404470…32800759138605081599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.053 Γ— 10⁹⁢(97-digit number)
40532132936690404470…32800759138605081601
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:57,757,101 XPMΒ·at block #6,814,126 Β· updates every 60s
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