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Block #1,633,669

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/18/2016, 7:56:07 AM Β· Difficulty 10.6026 Β· 5,191,325 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5c09a051a7784644bb9c7e48456b3d7dc1f54b118727acba66e15c0d62340144
View on Chainz β†—

Height

#1,633,669

Difficulty

10.602616

Transactions

2

Size

6.49 KB

Version

2

Bits

0a9a4511

Nonce

1,394,963,369

Timestamp

6/18/2016, 7:56:07 AM

Confirmations

5,191,325

Mined by

⛏️ P2SHAU9YmVNa61DG1eZqG4WQZYKvRYfNNwJ8QF

Merkle Root

dda17bc08fb3b7cf47a6b368110a5dbb538baaa173ca6647accbb5170843132d
Transactions (2)
Coinbasee196532f8e9c72…b4edf43f03ec69
1 in β†’ 1 out8.9600 XPM110 B
AU9YmVNa…fNNwJ8QF
bfa2a26b43efc8…fb8f308c7fcfa3
43 in β†’ 2 out10.0100 XPM6.29 KB
AGyiGjWR…yy2Gk1HVAdBkFe3y…8wvbTLE3
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.

1.540 Γ— 10⁹⁡(96-digit number)
15403060307751997813…05299097219579589119
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
1.540 Γ— 10⁹⁡(96-digit number)
15403060307751997813…05299097219579589119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.540 Γ— 10⁹⁡(96-digit number)
15403060307751997813…05299097219579589121
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
3.080 Γ— 10⁹⁡(96-digit number)
30806120615503995627…10598194439159178239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.080 Γ— 10⁹⁡(96-digit number)
30806120615503995627…10598194439159178241
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
6.161 Γ— 10⁹⁡(96-digit number)
61612241231007991254…21196388878318356479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.161 Γ— 10⁹⁡(96-digit number)
61612241231007991254…21196388878318356481
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
1.232 Γ— 10⁹⁢(97-digit number)
12322448246201598250…42392777756636712959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.232 Γ— 10⁹⁢(97-digit number)
12322448246201598250…42392777756636712961
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
2.464 Γ— 10⁹⁢(97-digit number)
24644896492403196501…84785555513273425919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.464 Γ— 10⁹⁢(97-digit number)
24644896492403196501…84785555513273425921
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:57,844,036 XPMΒ·at block #6,824,993 Β· updates every 60s
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