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Block #1,692,746

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/28/2016, 2:45:44 PM Β· Difficulty 10.6810 Β· 5,138,466 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
40ae9439a8c1dcb9784fdad747b29e11a99e31d9f6ecba80f8d49b1d2d0db0ca
View on Chainz β†—

Height

#1,692,746

Difficulty

10.681029

Transactions

1

Size

242 B

Version

2

Bits

0aae57ee

Nonce

255,747,028

Timestamp

7/28/2016, 2:45:44 PM

Confirmations

5,138,466

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

4fe757441923e2a6fd4e5af61232a001af294c2f9640d94dc9e9c0cc37ff080a
Transactions (1)
Coinbase4fe757441923e2…e9c0cc37ff080a
1 in β†’ 2 out8.7500 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

2.880 Γ— 10⁹⁴(95-digit number)
28803578282824878595…68929079276034679599
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
2.880 Γ— 10⁹⁴(95-digit number)
28803578282824878595…68929079276034679599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.880 Γ— 10⁹⁴(95-digit number)
28803578282824878595…68929079276034679601
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
5.760 Γ— 10⁹⁴(95-digit number)
57607156565649757191…37858158552069359199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.760 Γ— 10⁹⁴(95-digit number)
57607156565649757191…37858158552069359201
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
1.152 Γ— 10⁹⁡(96-digit number)
11521431313129951438…75716317104138718399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.152 Γ— 10⁹⁡(96-digit number)
11521431313129951438…75716317104138718401
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
2.304 Γ— 10⁹⁡(96-digit number)
23042862626259902876…51432634208277436799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.304 Γ— 10⁹⁡(96-digit number)
23042862626259902876…51432634208277436801
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
4.608 Γ— 10⁹⁡(96-digit number)
46085725252519805753…02865268416554873599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.608 Γ— 10⁹⁡(96-digit number)
46085725252519805753…02865268416554873601
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:57,893,844 XPMΒ·at block #6,831,211 Β· updates every 60s
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