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Block #1,745,243

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/2/2016, 3:38:40 PM Β· Difficulty 10.7188 Β· 5,099,600 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1ccb32681e48f1e6e45d79efa1c1259f59d45609a4f781c0773fcfc2830bbdf8
View on Chainz β†—

Height

#1,745,243

Difficulty

10.718844

Transactions

1

Size

242 B

Version

2

Bits

0ab8062b

Nonce

413,364,220

Timestamp

9/2/2016, 3:38:40 PM

Confirmations

5,099,600

Mined by

⛏️ P2SHAGkY5Euz5mzpuyGoaReCtspzag5TxsxHeG

Merkle Root

346a3560b4ef16b8ea30753c14a772f223ef080fab820c7653bb123c1decb739
Transactions (1)
Coinbase346a3560b4ef16…bb123c1decb739
1 in β†’ 2 out8.6900 XPM152 B
AGkY5Euz…5TxsxHeGALPu3s2c…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.

6.964 Γ— 10⁹⁴(95-digit number)
69648030289789709916…48735021110084619679
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
6.964 Γ— 10⁹⁴(95-digit number)
69648030289789709916…48735021110084619679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.964 Γ— 10⁹⁴(95-digit number)
69648030289789709916…48735021110084619681
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
1.392 Γ— 10⁹⁡(96-digit number)
13929606057957941983…97470042220169239359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.392 Γ— 10⁹⁡(96-digit number)
13929606057957941983…97470042220169239361
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
2.785 Γ— 10⁹⁡(96-digit number)
27859212115915883966…94940084440338478719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.785 Γ— 10⁹⁡(96-digit number)
27859212115915883966…94940084440338478721
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
5.571 Γ— 10⁹⁡(96-digit number)
55718424231831767933…89880168880676957439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.571 Γ— 10⁹⁡(96-digit number)
55718424231831767933…89880168880676957441
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
1.114 Γ— 10⁹⁢(97-digit number)
11143684846366353586…79760337761353914879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.114 Γ— 10⁹⁢(97-digit number)
11143684846366353586…79760337761353914881
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:58,003,153 XPMΒ·at block #6,844,842 Β· updates every 60s
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